Play a business simulator
Each short browser simulation turns pricing, staffing, capacity, quality, and cash-flow choices into measurable results.
Free Cash Flow (FCF) Margin & Cash Conversion Lab
Model free cash flow margins, cash conversion efficiency from net income, capital expenditure intensity, and Rule of 40 score with 5x5 sensitivity matrix analysis.
Sloan Ratio Calculator & Earnings Quality Forensic Lab
Evaluate Richard Sloan's accrual anomaly, paper accounting profits versus operational cash generation, and balance sheet earnings reversal risk.
Degree of Financial Leverage (DFL) Calculator & EPS Risk Lab
Model how fixed debt service and financing charges amplify earnings-per-share volatility, evaluate financial breakeven thresholds, and stress-test capital structure risk.
EV/FCF Multiple & Cash Valuation Lab
Model Enterprise Value to Free Cash Flow (EV/FCF) multiples, cash yield, capital structure debt bridges, and takeover target valuation.
Degree of Total Leverage (DTL) Calculator & Combined Risk Lab
Synthesize operating leverage (DOL) and financial leverage (DFL) into an enterprise multiplier to model top-line sales to bottom-line EPS sensitivity.
Defensive Interval Ratio (DIR) & Cash Runway Lab
Model Defensive Interval Ratio (DIR / DIP), daily cash burn rate, defensive quick asset reserves, and operational survival runway days without revenue.
Fixed Asset Turnover (FAT) & Capital Intensity Lab
Calculate Fixed Asset Turnover (FAT), Net PP&E utilization, capital intensity ratios, and capex expansion velocity across operating archetypes.
Cash Flow to Debt Ratio & Solvency Lab
Calculate Cash Flow to Debt Ratio (CFO / Total Debt), net debt payoff horizon, credit rating solvency, and debt coverage in a free business simulation lab.
Credit Spread & Default Probability Calculator
Calculate bond credit spreads (G-spread), risk-neutral implied default probability, cumulative default risk over maturity, and recovery risk premiums in an interactive fixed income lab.
Price-Volume-Mix (PVM) Calculator & Revenue Variance Lab
Deconstruct revenue and gross margin variances into Price, Volume, and Product Mix effects with interactive multi-product waterfall attribution.
Dividend Payout Ratio Calculator & Safety Lab
Model dividend payout ratios, earnings coverage cushions, dividend cut risk thresholds, and capital retention velocity across dividend aristocrats and high-yield equities.
Equity Multiplier Calculator & Financial Leverage Lab
Model financial leverage, assets-to-equity magnification, debt-to-equity bridge, and DuPont 3-step ROE expansion with dual 5x5 sensitivity matrices.
Cash Return on Invested Capital (CROIC) Calculator & Cash Moat Lab
Calculate Free Cash Flow to Invested Capital, CROIC vs. ROIC cash conversion quality, and economic cash spread over WACC across industry capital structures.
Effective Tax Rate & Corporate Tax Shield Lab
Model GAAP effective tax rate (ETR), cash taxes paid, deferred tax timing variance, debt interest tax shields, and pre-tax to net income waterfall.
Net Debt to EBITDA & Leverage Covenant Lab
Model Net Debt to EBITDA multiple, gross vs. net debt leverage bridge, bank credit covenant clearance headroom, and de-leveraging payoff horizons.
FCF Conversion Ratio & Cash Quality Lab
Model Free Cash Flow conversion from Net Income and EBITDA, diagnose non-cash accrual drags, measure CapEx absorption, and benchmark earnings quality.
Equity Ratio Calculator & Capital Structure Lab
Model stockholders' equity vs. total assets, calculate debt-to-assets absorption, evaluate the DuPont equity multiplier, and stress test balance sheet solvency.
Cash Conversion Efficiency Calculator & FCF Realization Lab
Model Cash Conversion Efficiency (CCE % = FCF ÷ Revenue), Operating Cash Flow realization, CapEx absorption, and working capital drag across operating business models.
Retained Earnings Calculator & Self-Funded Growth Lab
Model Ending Retained Earnings = Beginning + Net Income - Dividends, plowback retention rates, and sustainable self-funded growth capacity across operating scenarios.
Cost of Equity Calculator & Multi-Model Valuation Lab
Estimate Cost of Equity (Ke) using CAPM, Gordon Growth Model, and Bond Yield Plus Risk Premium methods with user-weighted triangulation and sensitivity matrices.
NOPAT & Economic Profit (EVA) Lab
Calculate Net Operating Profit After Tax (NOPAT = EBIT × (1 - t)), Return on Invested Capital (ROIC), Capital Charges, and Economic Value Added (EVA).
Equity Risk Premium (ERP) Multi-Model Lab
Estimate the market hurdle spread across Historical Realized, Damodaran Implied Forward DCF, and Ibbotson-Chen Supply-Side macroeconomic models.
Market Value Added (MVA) & Wealth Creation Lab
Model Market Value Added (MVA = Total Market Value - Invested Capital), single-period EVA, and discounted PV of future economic profits.
Internal Growth Rate (IGR) & Zero-Debt Lab
Model the maximum self-funded growth rate achievable strictly through retained earnings with zero debt or equity dilution, External Financing Needed (EFN), and Higgins SGR contrast.
Residual Income Valuation (EBO Model) Lab
Estimate intrinsic equity value, equity capital charges, and justified P/B multiples using Clean Surplus Accounting and competitive persistence decay.
Adjusted Present Value (APV) Valuation Lab
Model Myers (1974) Adjusted Present Value, unlevered DCF cash flows, interest tax shields with dynamic debt paydown, and financial distress costs.
Fuller-Hsia H-Model Dividend Discount Lab
Model Fuller-Hsia two-stage equity valuation, linear dividend growth fade, terminal value, market-implied cost of equity, and discrete DCF schedules.
Asian Option Pricing Lab
Value arithmetic and geometric Asian options with Kemna-Vorst closed forms and Turnbull-Wakeman moment matching, quantifying volatility dampening.
Lookback Option Pricing Lab
Price floating and fixed strike lookback options using Goldman-Sosin-Gatto and Conze-Viswanathan analytical formulas with discrete monitoring adjustments.
Margrabe Exchange Option Lab
Value options to exchange one asset for another with William Margrabe's (1978) closed-form formula, combined spread volatility, and cross-asset Greeks.
Compound Option Pricing Lab (Geske 1979)
Value options on options across Call-on-Call, Put-on-Call, Call-on-Put, and Put-on-Put with Robert Geske's (1979) model, critical boundary S*, and staged real options.
Chooser Option Pricing Lab (Rubinstein 1991)
Value simple and complex chooser options (as-you-like-it options) with Mark Rubinstein's (1991) model, critical hurdle S*, Greeks, and straddle discount analysis.
Bermudan Option Pricing & Early Exercise Lab
Price Bermudan options with discrete early-exercise schedules using recombining binomial lattices, backward induction, early exercise boundaries, and American vs European decomposition.
Forward Start Option Pricing & Reset Lab (Rubinstein 1991)
Price forward start options with future strike determination date t1 and moneyness multiple alpha under Mark Rubinstein's (1991) model, normalized unit pricing, and cliquet structures.
Gap Option Pricing & Payoff Discontinuity Lab
Price European gap calls and puts with dual strikes (K1 trigger hurdle, K2 payoff strike). Model negative option values, jump discontinuities, and Delta/Gamma cliff risks.
Rainbow Option Pricing & Multi-Asset Correlation Lab
Price multi-asset rainbow options on the maximum (Best-of) or minimum (Worst-of) of two risky assets using Johnson (1987) closed forms, bivariate normal CDFs, and correlation Greeks.
Basket Option Pricing & Portfolio Correlation Lab
Value multi-asset equity basket options. Model moment matching approximations, diversification discounts, cross-asset correlation dispersion, and Component Greeks.
Digital Option Pricing & Binary Greeks Lab
Value cash-or-nothing and asset-or-nothing binary options. Analyze extreme expiry pin risk, Dirac delta Greeks, and tight vanilla call spread static replication.
Quanto Option Pricing & FX Correlation Lab
Value cross-currency quanto derivatives with fixed guaranteed exchange rates. Model Girsanov quanto drift adjustments, equity-FX correlation risk, and cross-currency Greeks.
Power Option Pricing & Convexity Greeks Lab
Value non-linear power contracts with payoff exponents α. Model Itô volatility magnification, non-linear super-convexity, leverage explosions, and higher-order Greeks.
Cliquet Option Pricing & Ratchet Equity Lab
Value multi-period cliquet (ratchet) equity options. Model periodic strike resets, local return caps and floors, forward-start option series, and structured notes.
Variance Swap & Volatility Derivatives Lab
Value institutional variance swaps. Model Demeterfi et al. (1999) log-contract replication strips, fair variance strikes, vega notional conversions, and capped payoffs.
Autocallable Structured Note & Phoenix Lab
Value autocallable notes and Phoenix reverse convertibles. Model periodic early redemption triggers, memory coupons, European/American knock-in barriers, and duration risk.
Credit Default Swap (CDS) Pricing & Hazard Rate Lab
Value single-name Credit Default Swaps, ISDA standard coupons (100/500 bps), upfront payment settlement, hazard rate bootstrapping, survival curves, and CS01/DV01 risk.
Credit Valuation Adjustment (CVA) & XVA Lab
Model OTC derivative counterparty credit risk, Expected Exposure profiles (EE, EPE, PFE 95th/99th), unilateral CVA, DVA, Bilateral BCVA, and ISDA CSA collateral netting.
Forward Rate Agreement (FRA) Pricing & Hedging Lab
Value money market Forward Rate Agreements (FRAs), no-arbitrage forward rate curves, in-advance discounted settlement payoffs, and borrower/lender hedging strategies.
Interest Rate Cap, Floor & Collar Pricing Lab
Value interest rate caps, floors, and zero-cost collars using Black-76, model caplet amortization strips, cap-floor parity, and Vega/Theta risk management.
European Swaption Pricing Lab (Black-76 & Bachelier)
Price interest rate payer and receiver swaptions across Expiry × Tenor structures, model swap annuities (PVBP), and compare Black-76 vs Bachelier normal models.
Constant Maturity Swap (CMS) & Convexity Adjustment Lab
Model Constant Maturity Swaps (CMS), calculate numeraire-change convexity adjustments, price CMS caps and floors, and structure curve spread options.
Bermudan Swaption Pricing Lab (Hull-White Tree)
Price callable and Bermudan interest rate swaptions using a 1-factor Hull-White trinomial tree, model early exercise boundaries, and calculate flexibility premiums.
Corporate Debt Restructuring & Debt-to-Equity Swap Lab
Model distressed corporate debt recapitalizations, creditor haircuts, debt-to-equity swaps (DES), existing shareholder dilution, and post-restructuring solvency covenants.
Convertible Bond Pricing & Greeks Lab
Value hybrid convertible bonds, conversion parity, straight debt investment floors, bifurcation option premiums, conversion premiums, and arbitrage delta hedging.
Bond Convexity & Price Volatility Lab
Calculate analytical bond convexity, modified duration, dollar convexity, and compare first-order linear duration vs. second-order Taylor series approximations under rate shocks.
Barbell vs. Bullet Bond Strategy Lab
Construct duration-matched barbell and bullet fixed income portfolios, analyze the barbell convexity premium, model yield giveup drag, and simulate returns across curve shifts.
Key Rate Duration Lab
Quantify key rate duration (KRD) vectors across benchmark tenors (2Y, 5Y, 10Y, 30Y), model non-parallel yield curve reshaping, and evaluate multi-bond portfolio shaping risk.
Spot vs. Forward Rate Curve Lab
Bootstrap zero-coupon spot yield curves from coupon-bearing par bonds, extract implied forward rates (1y1y, 2y3y, 5y5y), and model term premium dynamics.
Nelson-Siegel & Svensson Curve Lab
Calibrate Nelson-Siegel and Svensson parametric yield curves, decompose Level, Slope, and Curvature factors, and derive instantaneous forward curves.
Z-Spread, OAS & ASW Spread Lab
Decompose bond credit risk by discounting cash flows over the spot curve. Compute Z-spread, Option-Adjusted Spread (OAS), and Par-Par Asset Swap Spread (ASW).
Box Spread Arbitrage Lab
Model 4-legged options box spreads, calculate implied borrowing/lending rates, theoretical bounds, American early exercise risk, and slippage frictions.
Iron Condor & Credit Spread Lab
Model 4-legged delta-neutral Iron Condors, evaluate Probability of Profit (POP), credit collection, max risk, and portfolio Greeks across time.
Butterfly Spread Strategy & Greeks Lab
Model 3-strike options butterfly structures (1-2-1), Black-Scholes Greeks, asymmetric broken-wing variations, pin risk, and time-decay acceleration.
Straddle & Strangle Strategy Lab
Model pure volatility options plays, binary event expected moves, post-earnings IV crush, gamma-theta trade-offs, and dual breakeven boundaries.
Calendar & Time Decay Options Lab
Model horizontal time spreads, differential theta acceleration, implied volatility term structure skew, and front-month expiration mark-to-market payoffs.
Ratio Spread & Volume Backspread Lab
Model 1:2 Call/Put front ratio spreads, 2:1 volatility backspreads, asymmetric tail risk, naked strike breakevens, and Black-Scholes Greeks.
Condor Spread Strategy Lab
Model 4-strike Long & Short Condor spreads, flat profit plateau (K2 to K3), dual breakevens, defined risk limits, and Black-Scholes Greeks.
Seagull Spread Strategy Lab
Model 3-strike Bull & Bear Seagull spreads, zero-cost FX corridors, asymmetric tail risk, breakevens, and Black-Scholes Greeks.
Collar Strategy Lab
Model Protective Collar options strategies, zero-cost hedging corridors, floor protection, capped upside, net Greeks, and Black-Scholes pricing.
Strip & Strap Options Lab
Model asymmetric 2:1 Strip (bearish) and Strap (bullish) options strategies, directional volatility tilt, dual breakevens, and Black-Scholes Greeks.
Iron Butterfly Strategy Lab
Model 4-leg Iron Butterfly credit structures: short ATM straddle core, long OTM wings, peak profit apex, defined risk bounds, and Black-Scholes Greeks.
Christmas Tree Spread Lab
Model asymmetric 3-strike option ladders (+1 K1, -1 K2, -1 K3): low net debit entry, directional bias with defined risk, peak profit, and Black-Scholes Greeks.
Risk Reversal Strategy Lab
Model directional synthetic options setups and FX 25-delta volatility skew: call vs put parity, zero-cost corridors, and Black-Scholes Greeks.
Jelly Roll Strategy Lab
Master 4-legged calendar synthetic loans, put-call parity theoretical pricing, implied financing rates, and American early assignment risk.
Dispersion Trading Strategy Lab
Model index vs basket volatility relative value, implied correlation calculation, vega-neutral hedging, and correlation risk premium (CRP).
Synthetic Futures Strategy Lab
Master Put-Call Parity synthetic replication (+C/-P), cost of carry forward pricing, margin efficiency, and zero-vega linear delta tracking.
Breeden-Litzenberger Density Lab
Extract model-free risk-neutral probability density functions (RND) using second partial derivative curvature and butterfly option replication.
Vanna-Volga Pricing & Hedging Lab
Price FX and equity options using the Vanna-Volga method. Compute smile adjustments, Vega, Vanna, and Volga hedges with 25-delta risk reversals.
Implied Volatility Surface & SVI Lab
Model institutional 3D volatility surfaces and Gatheral SVI calibration. Analyze strike skews, term structure contango/backwardation, and calendar no-arbitrage bounds.
Volatility Cone & Realized Vol Lab
Analyze institutional volatility cones, multi-horizon realized volatility percentiles, estimator efficiencies (Parkinson, Garman-Klass, Yang-Zhang), and Volatility Risk Premium (VRP).
Spread Option Pricing Lab
Price two-asset European spread options with non-zero strikes using Kirk's (1995) approximation. Model crack spreads, spark spreads, cross-asset Greeks, and correlation sensitivities.
Dupire Local Volatility Lab
Extract Bruno Dupire's (1994) local volatility surface from Black-Scholes implied variance smiles. Analyze the factor-of-two slope rule, calendar monotonicity, and butterfly convexity.
CBOE VIX Index Lab
Calculate the official CBOE Volatility Index (VIX) from discrete options chains. Explore log-contract replication with 1/K² weights, zero-bid truncation, and 30-day roll interpolation.
Volatility Swap Lab
Price pure volatility swaps and model Jensen's inequality convexity drag. Analyze Brockhaus-Long analytical Taylor expansions, linear vs. convex variance payoffs, and mark-to-market trajectories.
Correlation Swap Lab
Price correlation swaps, evaluate Sebastien Bossu implied correlation replication from index vs basket variance, model the Correlation Risk Premium (CRP), and track mark-to-market curves.
Corridor Variance Swap Lab
Price conditional corridor variance swaps and downside semi-variance swaps. Model Peter Carr & Roger Lee bounded replication strips, strike discounts, and barrier pin risk.
Forward Volatility (FVA) Lab
Price Forward Volatility Agreements (FVA) and forward starting variance swaps. Model calendar variance replication, forward convexity drag, and term structure roll-down carry.
VIX Futures & Options Lab
Price VIX futures and options. Model mean reversion, term structure roll yield, Black-76 option Greeks, positive volatility skew, and ETP drag.
CPPI Portfolio Insurance Lab
Simulate Constant Proportion Portfolio Insurance (CPPI). Model dynamic floor protection, cushion leverage, cash-lock risk, and gap crash events.
OBPI Portfolio Insurance Lab
Price Option-Based Portfolio Insurance (OBPI). Model protective puts, 90/10 capital protected notes, participation rates, and theta decay.
TIPP Portfolio Insurance Lab
Model Time-Invariant Portfolio Protection (TIPP). Simulate ratcheted trailing floors, high-water marks, cash-lock risk, and CPPI comparisons.
Risk Parity & ERC Lab
Model Risk Parity and Equal Risk Contribution (ERC) portfolios. Compare 60/40 asset allocations, risk budgets, leverage, and macro regimes.
Hierarchical Risk Parity Lab
Model Hierarchical Risk Parity (HRP) portfolios. Compare López de Prado tree clustering, recursive bisection, Markowitz CLA, and risk budgets.
Maximum Diversification Lab
Model the Most Diversified Portfolio (MDP) and Diversification Ratio (DR). Compare Choueifaty equi-correlation, risk parity, HRP, and Markowitz CLA.
Resampled Efficient Frontier Lab
Model Michaud's Resampled Efficient Frontier. Compare Monte Carlo parameter uncertainty, classical Markowitz CLA, and robust asset allocations.
Ledoit-Wolf Covariance Shrinkage Lab
Model Ledoit-Wolf optimal covariance shrinkage, Random Matrix Theory, and Marcenko-Pastur bounds. Stabilize Markowitz portfolios under sample noise.
Kelly Criterion Portfolio Lab
Model continuous multi-asset Kelly optimization, fractional Kelly leverage, logarithmic capital growth, and drawdown risk.
Fundamental Law of Active Management Lab
Model Grinold & Kahn Information Ratio, transfer coefficient, breadth compression, and active alpha forecasting.
Brinson Portfolio Attribution Lab
Model Brinson-Hood-Beebower (BHB) and Brinson-Fachler (BF) portfolio attribution, sector allocation, selection, and interaction effects.
Barra Factor Risk & Tracking Error Lab
Model Barra multi-factor risk, active tracking error, systematic factor exposures, specific risk, and Euler risk contributions.
Almgren-Chriss Optimal Execution Lab
Model Almgren-Chriss optimal liquidation, permanent and temporary market impact, trading urgency, and execution frontiers.
Sharpe Style Analysis (RBSA) Lab
Model William Sharpe returns-based style analysis, effective asset allocation, R² style fit, active alpha, and rolling style drift.
Copula & Tail Dependence Portfolio Lab
Model Gaussian, Student-t, Clayton, and Gumbel copulas, lower and upper tail dependence, joint default risk, and systemic crash contagion.
CVaR & Expected Shortfall Optimization Lab
Model Rockafellar-Uryasev CVaR portfolio optimization, Euler component tail risk decomposition, and Basel FRTB Expected Shortfall.
GARCH(1,1) Volatility Forecasting Lab
Model Bollerslev GARCH(1,1) and GJR-GARCH volatility clustering, shock persistence, half-life, news impact curves, and term structure forecasts.
Variance Gamma (VG) Option Pricing Lab
Model Madan-Carr-Chang pure jump Lévy dynamics, stochastic operational time subordination, leptokurtic return densities, and Fourier option pricing.
Kou Jump-Diffusion Option Pricing Lab
Model Steven Kou (2002) double exponential jump-diffusion dynamics, asymmetric upward/downward jump decays, memoryless overshoot property, and Fourier option pricing.
Bates Model Option Pricing Lab
Model David Bates (1996) stochastic volatility with jumps, combining Heston CIR variance diffusion and Merton Poisson jumps to resolve short-tenor skews.
CEV Model Option Pricing Lab
Model John Cox (1975) Constant Elasticity of Variance local volatility diffusion, non-central chi-square option pricing, default risk, and leverage skews.
Merton Portfolio Choice & Consumption Lab
Model Robert C. Merton's (1971) continuous-time portfolio choice, optimal risky share rule, and dynamic lifetime consumption under CRRA utility.
Carr-Madan Option Replication Lab
Model Peter Carr & Dilip Madan's (2001) static spanning theorem, replicate arbitrary European payoffs, and synthesize model-free VIX variance strips.
Kyle's Lambda & Market Microstructure Lab
Model Pete Kyle (1985) price impact, Glosten-Milgrom adverse selection spreads, Roll effective spread, and Bayesian order flow price discovery.
Pairs Trading & Statistical Arbitrage Lab
Model Marco Avellaneda and Jeong-Hyun Lee (2010) Ornstein-Uhlenbeck spread dynamics, s-scores, and market-neutral backtest returns.
VPIN & Order Flow Toxicity Lab
Model David Easley, Marcos López de Prado, and Maureen O'Hara (2012) Volume-Synchronized Probability of Toxicity (VPIN), bulk volume classification, and flash crash liquidity risks.
Avellaneda-Stoikov Market Making Lab
Model Marco Avellaneda and Sasha Stoikov (2008) high-frequency market making, reservation price skewing, optimal bid-ask spreads, and inventory penalty dynamics.
Hasbrouck Information Share Lab
Model Joel Hasbrouck (1995) Information Share and Gonzalo-Granger Component Share price discovery across fragmented equity, futures, and crypto markets.
Huang-Stoll Spread Decomposition Lab
Decompose the quoted bid-ask spread into adverse selection, inventory risk, and order processing components using the Huang-Stoll (1997) structural model.
Yang-Zhang Range Volatility Lab
Estimate historical volatility with 8x to 14x greater statistical efficiency using Dennis Yang and Qiang Zhang's (2000) jump- and drift-adjusted OHLC model.
MRR Spread Decomposition Lab
Deconstruct security price changes into adverse selection trade surprises, transitory order processing friction, and public news shocks using the Madhavan-Richardson-Roompack (1997) model.
Bipower Variation & Jump Test Lab
Disentangle continuous price volatility from discrete jumps using Barndorff-Nielsen & Shephard (2004, 2006) Realized Bipower Variation and BNS jump tests.
Order Flow Imbalance (OFI) Lab
Quantify limit order book dynamics and high-frequency price impact using Rama Cont, Kukanov, and Stoikov's (2014) Order Flow Imbalance (OFI) model.
Gatheral Transient Impact Lab
Model transient market impact, order book resiliency decay, and absence of price manipulation using Jim Gatheral's (2010) optimal execution framework.
Roll (1984) Effective Spread Lab
Estimate effective bid-ask spreads and microstructure noise from transaction price serial covariance using Richard Roll's (1984) classic model.
Corwin-Schultz (2012) High-Low Spread Lab
Estimate bid-ask spreads and liquidity from daily high and low prices using Angelo Corwin and Paul Schultz's (2012) high-low range microstructure model.
Glosten-Milgrom (1985) Microstructure Lab
Simulate sequential trade arrival, Bayesian quote updating, information asymmetry, and bid-ask spread decay using the classic Glosten-Milgrom (1985) model.
EKOP PIN (1996) Probability of Informed Trading Lab
Estimate the Probability of Informed Trading (PIN) from daily buy and sell order imbalances using the classic Easley, Kiefer, O'Hara, and Paperman (1996) model.
Hasbrouck (1991) Trade VAR & Price Impact Lab
Measure the permanent and transitory price impact of trades and private information variance using Joel Hasbrouck's (1991) Vector Autoregression (VAR) model.
Kyle-Obizhaeva (2016) Microstructure Invariance Lab
Model Pete Kyle and Anna Obizhaeva's (2016) Market Microstructure Invariance laws: invariant bet rates, trade sizes, transaction costs, and price impact scaling.
Engle-Russell (1998) ACD Duration Model Lab
Model Robert Engle and Jeffrey Russell's (1998) Autoregressive Conditional Duration (ACD) point process, trade arrival timing, hazard rates, and instantaneous volatility.
Ho-Stoll (1981) Market Making Lab
Model Thomas Ho and Hans Stoll's (1981) optimal dealer pricing: inventory risk, asymmetric bid-ask quote shading, and reservation price dynamics.
Hawkes (1971) High-Frequency Process Lab
Model Alan Hawkes' (1971) self-exciting point processes: high-frequency trade clustering, branching ratios, endogenous cascades, and flash crashes.
Bouchaud Propagator Market Impact Lab
Model Bouchaud's (2004) market impact propagator: long-memory order flow, power-law kernel decay, apparent vs bare impact, and critical diffusivity.
Cartea-Jaimungal (2014) Market Making Lab
Model Cartea and Jaimungal's (2014) optimal market making with alpha signals, Ornstein-Uhlenbeck drift, inventory risk, and adverse selection.
Rough Volatility & Bergomi Lab
Model Gatheral's (2018) Rough Volatility: fractional Brownian motion, Hurst parameter H < 0.5, power-law ATM skew explosion, and Rough Bergomi.
Guéant-Tapia-Manziadi (2012) Market Making Lab
Model Guéant, Tapia, and Manziadi's (2012) closed-form market making: matrix exponential HJB solution, inventory bounds, and optimal spreads.
Cont-Stoikov (2010) Order Book Lab
Model Cont, Stoikov, and Talreja's (2010) limit order book dynamics: Markovian queue depletion, order imbalance, and price move probabilities.
Gatheral SVI Volatility Lab
Calibrate Gatheral's (2004) SVI volatility smile, analyze butterfly arbitrage conditions, evaluate Roger Lee wing bounds, and inspect implied density.
Cont-de Larrard (2013) Order Book Lab
Model Cont and de Larrard's (2013) Markovian limit order book diffusion limit, harmonic price move probabilities, duration tails, and micro-volatility.
Carr-Madan (1999) FFT Option Pricing Lab
Price options across full strike surfaces simultaneously in O(N log N) using Carr-Madan (1999) Fast Fourier Transform inversion of risk-neutral characteristic functions.
Fang-Oosterlee (2008) COS Option Pricing Lab
Price European options with exponential spectral convergence and closed-form Greeks using Fang and Oosterlee's (2008) Fourier-Cosine series expansion method.
Longstaff-Schwartz (2001) LSM Option Pricing Lab
Value American options by simulation using the Longstaff-Schwartz (2001) Least Squares Monte Carlo (LSM) method with backward induction, dynamic exercise boundaries, and OLS regression.
Brace-Gatarek-Musiela (BGM / LMM) Market Model Lab
Simulate high-dimensional forward interest rate term structures using the Brace-Gatarek-Musiela (1997) LIBOR Market Model, Rebonato humped volatilities, predictor-corrector drift stepping, and swaptions.
Leland (1994) Corporate Debt & Endogenous Default Lab
Model continuous-time corporate debt valuation, smooth-pasting endogenous bankruptcy barriers, debt tax shield trade-offs, and Leland-Toft (1996) credit spread term structures.
Duffie-Singleton (1999) Credit Risk & Defaultable Bond Lab
Value defaultable corporate bonds, credit spread term structures, and hazard rates using Darrell Duffie and Kenneth Singleton's (1999) Recovery of Market Value framework.
Jarrow-Lando-Turnbull (1997) Credit Rating Migration Lab
Model Markov chain credit rating migrations, absorbing default states, physical vs risk-neutral transition matrices, and CreditMetrics CreditVaR.
Vasicek (2002) Credit Portfolio & Basel Capital Lab
Simulate asymptotic single risk factor (ASRF) credit loss distributions, 99.9% VaR, Expected Shortfall, and Basel II/III IRB regulatory capital.
David X. Li (2000) Gaussian Copula CDO Tranche Pricing Lab
Price synthetic CDO tranches, compute breakeven credit spreads, and model default correlation smiles with Li's Gaussian copula.
CreditMetrics (1997, J.P. Morgan) Portfolio CreditVaR Lab
Simulate multi-obligor credit portfolio risk, rating migrations, asset correlation, and CreditVaR using J.P. Morgan's CreditMetrics.
CreditRisk+ (1997, CSFP) Actuarial Credit Portfolio Lab
Model Poisson mixture default processes, Gamma-distributed systematic factor clustering, and exact loss distributions via Panjer recursion.
KMV Credit Portfolio Model & Expected Default Frequency (EDF™) Lab
Simulate Merton structural asset inversion, empirical Expected Default Frequency (EDF), and multi-obligor portfolio CreditVaR using the Kealhofer-McQuown-Vasicek framework.
CreditPortfolioView (McKinsey / Wilson) Macro Credit Lab
Simulate multi-factor macroeconomic logit default models, credit cycle indices, stress-tested migration matrices, and portfolio CreditVaR.
Heath-Jarrow-Morton (1992) Forward Rate Lab
Simulate no-arbitrage instantaneous forward rate curves, multi-factor volatility structures, Monte Carlo martingale tests, and swaption pricing under HJM (1992).
Black-Karasinski (1991) Lognormal Model Lab
Construct calibrated lognormal short-rate trinomial trees via Arrow-Debreu forward induction, price callable bonds, and analyze negative convexity.
Two-Factor Hull-White (G2++) Model Lab
Simulate two-additive-factor Gaussian short rates, analyze yield curve twisting and slope dynamics, and price European swaptions via 1D quadrature.
CIR++ Model Lab
Calibrate market yield curves via deterministic shifts, verify Feller positivity conditions, and price European swaptions analytically via Jamshidian decomposition.
Cheyette Model Lab
Simulate Oren Cheyette's separable volatility framework reducing Heath-Jarrow-Morton forward rates to a 2D Markovian state space (x, y), with exact zero-coupon bond pricing and Jamshidian swaptions.
Multi-Curve & Basis Swap Lab
Model the post-2008 multi-curve framework: OIS/SOFR collateral discounting, distinct forward rate projections, breakeven tenor basis swaps (3M vs 6M), and single-curve mispricing.
Cross-Currency Basis Swap Lab
Model cross-currency basis swaps (XCS), Covered Interest Rate Parity (CIP) deviations, Vladimir Piterbarg foreign collateral discounting, and USD funding premia.
MBS Prepayment & Convexity Lab
Model Agency MBS pass-through cash flows, Richard-Roll & PSA prepayment S-curves, SMM/CPR conversions, negative convexity, and Option-Adjusted Spread (OAS).
CMO Tranche Waterfall & Structuring Lab
Model CMO tranche waterfalls, sequential pay structures, PAC collar bands, companion tranches, Z-accruals, and IO/PO mortgage strips.
CLO Tranche Waterfall & Coverage Test Lab
Model CLO tranche waterfalls, Overcollateralization (OC) and IC tests, cash diversion triggers, sequential debt paydowns, and equity tranche IRR.
Credit Card ABS & Excess Spread Lab
Model Credit Card Asset-Backed Securities (ABS) revolving master trusts, excess spread covenants, Early Amortization triggers, and MPR paydown velocity.
CMBS Conduit & Defeasance Lab
Model Commercial Mortgage-Backed Securities (CMBS) conduit pools, Debt Yield, Defeasance, Appraisal Reduction Amounts (ARA), and tranche waterfalls.
Auto Loan ABS & CNL Waterfall Lab
Model Auto Loan Asset-Backed Securities (ABS), Absolute Prepayment Speed (ABS), Cumulative Net Loss (CNL) curves, and tranche waterfalls.
Equipment Lease ABS & Residual Value Lab
Model Equipment Lease Asset-Backed Securities (ABS), Fair Market Value (FMV) residuals, DRV haircuts, turn-back risk, and tranche waterfalls.
WBS Franchise Royalty Securitization Lab
Model Whole Business Securitization (WBS), franchise royalty waterfalls, DSCR cash trapping, rapid amortization triggers, and post-ARD step-up interest.
SLABS & Student Loan Waterfall Lab
Model Student Loan Asset-Backed Securities (SLABS), FFELP government guarantees, SAP subsidies, parity ratios, cohort default curves, and turbo waterfalls.
Barrier Option Pricing Lab
Value European knock-in and knock-out barrier options, analyze barrier pin risk, discontinuous Greeks, and in-out parity with closed-form formulas.
Black-76 Futures Option Lab
Value options on futures contracts, commodity forwards, interest rate caplets, and swaptions using Fischer Black's (1976) forward pricing framework.
Bjerksund-Stensland Option Lab
Model American option early exercise boundaries, analytical trigger points, and early exercise premiums with the Bjerksund-Stensland (1993) closed-form approximation.
Barone-Adesi Whaley American Option Lab
Model American option early exercise premiums, optimal exercise boundaries, and cost of carry dynamics with the Barone-Adesi & Whaley (1987) quadratic approximation.
Garman-Kohlhagen FX Option Lab
Simulate the Garman-Kohlhagen (1983) FX option pricing model, covered interest parity, dual interest rate Greeks, and forward delta surfaces in an interactive lab.
Merton Jump-Diffusion Lab
Simulate Robert Merton's (1976) jump-diffusion model, compound Poisson jump arrivals, lognormal jump sizes, and volatility smile in an interactive lab.
SABR Stochastic Volatility Model Lab
Model SABR stochastic volatility, Hagan asymptotic Black implied volatility smile, backbone dynamics, and CEV elasticity in an interactive quantitative lab.
Heston Stochastic Volatility Lab
Simulate the Heston (1993) stochastic volatility model. Solve options via Fourier inversion, generate the Black-Scholes implied volatility smile/skew, and verify CIR variance dynamics.
BDT Interest Rate Lattice Lab
Simulate the Black-Derman-Toy (BDT 1990) lognormal short-rate binomial lattice. Calibrate to the spot yield curve, price callable bonds, and analyze embedded options and negative convexity.
Hull-White Interest Rate Model Lab
Simulate the Hull-White (1990) one-factor short-rate model. Calibrate time-dependent drift theta(t) to fit the market yield curve with zero error, price bond options, and analyze trinomial trees.
CIR Interest Rate Model Lab
Simulate the Cox-Ingersoll-Ross (CIR 1985) square-root diffusion short-rate model. Check Feller condition non-negativity, derive analytical zero-coupon bonds, and evaluate term structure curves.
Vasicek Short-Rate Model Lab
Simulate Oldrich Vasicek's (1977) Ornstein-Uhlenbeck stochastic interest rate model. Compute analytical zero-coupon bond prices, term structure curves, mean-reversion speed, and convexity drag.
Ohlson Clean Surplus Lab
Value equity using James Ohlson's (1995) Clean Surplus Model and Linear Information Dynamics (LID). Model abnormal earnings persistence (ω), non-accounting signals (v_t), and book value convergence.
Bond Portfolio Immunization Lab
Model institutional asset-liability management (ALM) under Redington conditions. Calculate barbell duration matching, convexity surplus, and Fong-Vasicek M² risk across yield shifts.
Walter's Model of Dividend Policy Lab
Determine optimal dividend payout ratios and share valuation using Walter's Model. Compare growth (r > ke), normal (r = ke), and declining (r < ke) corporate regimes.
Cox-Ross-Rubinstein Binomial Option Pricing Lab
Price American and European options using the Cox-Ross-Rubinstein (1979) binomial lattice model. Visualize recombining trees, backward induction, early exercise, and delta hedging.
Treynor-Black Active Portfolio Management Lab
Integrate micro security analysis with macro index tracking. Model security appraisal ratios, unsystematic risk penalties, optimal active allocation, and Sharpe ratio expansion.
Modified Jones Model & Discretionary Accruals Lab
Decompose total accruals into non-discretionary and discretionary components using the Dechow et al. (1995) econometric model to detect earnings manipulation and channel stuffing.
Black-Litterman Portfolio Optimization Lab
Model Bayesian portfolio optimization, reverse optimization equilibrium returns, subjective investor views, confidence scaling, and active asset allocation tilts.
Debt Capacity & Maximum Debt Sizing Lab
Model maximum enterprise borrowing capacity, leverage bottlenecks, interest coverage constraints, and debt sizing covenants.
Fama-French 3-Factor & 5-Factor Asset Pricing Lab
Model multi-factor expected returns, size (SMB) and value (HML) premia, profitability (RMW), investment (CMA), and multi-factor alpha.
Merton Structural Credit Model & Distance to Default Lab
Model Merton (1974) option-theoretic credit risk, implied asset volatility, Distance to Default (DD), Expected Default Frequency (EDF), and credit spreads.
Ohlson O-Score Bankruptcy Probability Lab
Model 2-year logistic bankruptcy probability, 9-factor econometric distress terms, leverage pressure, and insolvency default thresholds.
Zmijewski X-Score Distress Lab
Model financial distress and default probability using Zmijewski probit analysis, ROA profitability, leverage, and current liquidity ratios.
Earnings Yield & Equity Risk Premium Lab
Calculate Earnings Yield (E/P), the inverse P/E ratio, Fed Model equity risk premium spread over 10-year Treasuries, and inflation-adjusted real yields.
Dividend Coverage Ratio & FCF Safety Lab
Model Dividend Coverage Ratio (DCR = EPS ÷ DPS), Free Cash Flow coverage multiples, cash safety buffer headroom, and dividend cut risk.
Working Capital Funding Gap Calculator & Credit Line Lab
Model the dollar gap between operating assets (AR + Inventory) and spontaneous vendor financing (AP), determine revolving credit line needs, and stress-test growth liquidity requirements.
Working Capital Turnover Calculator & Capital Velocity Lab
Model Working Capital Turnover (Revenue ÷ NWC), Days Working Capital (DWC), capital support capacity, and overtrading liquidity risk across operating scenarios.
Cash Ratio & Liquidity Coverage Lab
Calculate Cash Ratio, pure liquidity runway, instant debt coverage, and cash buffer surplus in an interactive corporate treasury simulation lab.
Cost of Debt & After-Tax Interest Shield Lab
Calculate pre-tax and after-tax cost of debt, multi-tranche blended borrowing rates, credit rating spreads, and Section 163(j) corporate interest tax shields.
Tobin's Q & Asset Replacement Valuation Lab
Calculate Tobin's Q ratio, Chung-Pruitt approximation, physical asset reproduction costs, franchise moat spreads, and corporate takeover incentives.
Print a student worksheet
Use a worksheet to record a starting strategy, compare results, and reflect on the next decision.
Classroom and comparison collections
- Business simulations hub
- Break-even, unit economics, and pricing calculators
- 12-Month pro-forma financial model and cash flow generator
- Pricing strategy simulator and price elasticity lab
- Break-even matrix and CVP sensitivity analysis lab
- Unit economics, customer acquisition cost (CAC), and LTV cohort lab
- Working capital and cash conversion cycle (CCC) simulator
- Staffing capacity, labor cost percentage, and overtime simulator
- Business valuation, SDE multiples, and deal structure lab
- Cost of quality (COQ), PAF model, and defect prevention lab
- Business risk, operating leverage, and financial resilience stress-test lab
- Hospitality RevPAR, TrevPAR, ADR yield, and restaurant Prime Cost lab
- Service business utilization, billing realization, and Effective Hourly Rate (EHR) lab
- Capital budgeting, Net Present Value (NPV), and Internal Rate of Return (IRR) lab
- Marketing ROI, customer acquisition funnel, and Return on Ad Spend (ROAS) lab
- Inventory Economic Order Quantity (EOQ), safety stock, and Reorder Point (ROP) lab
- Strategic decision matrix, multi-criteria decision analysis (MCDA), and tradeoff lab
- DuPont analysis, Return on Equity (ROE) decomposition, and financial leverage lab
- Overall Equipment Effectiveness (OEE), Availability, and Six Big Losses lab
- Customer churn rate, Net Revenue Retention (NRR), and cohort decay lab
- Sales mix variance, multi-product contribution margin, and break-even allocation lab
- Weighted Average Cost of Capital (WACC), CAPM, and capital structure lab
- Queuing theory, M/M/c wait times, and service bottleneck lab
- SaaS metrics, Rule of 40, and Burn Multiple capital efficiency lab
- Safety stock, lead time variability, and stockout risk lab
- Takt time, line balancing, and bottleneck pacing lab
- Commercial real estate valuation, Cap Rate, and DSCR lab
- Scenario planning, Bear/Base/Bull cases, and Tornado sensitivity lab
- CAC payback period, blended vs. paid CAC, and marketing attribution lab
- Financial ratios, Altman Z-Score default risk, and solvency lab
- Employee turnover cost, vacancy ramp drag, and retention ROI lab
- Inventory turnover, GMROI retail productivity, and shrinkage lab
- E-commerce conversion funnel, cart abandonment, and CRO lift lab
- Equipment lease vs. buy, loan amortization, and NPV tax shield lab
- Make vs. buy, crossover volume, and strategic sourcing lab
- Sales pipeline velocity, quota coverage, and win rate lab
- Process capability (Cp, Cpk), Six Sigma DPMO, and defect lab
- Consulting project profitability, Effective Hourly Rate (EHR), and scope creep lab
- M&A accretion / dilution, financing mix, and synergies lab
- Restaurant food cost percentage, recipe plate costing, and variance lab
- Enterprise risk matrix, Annualized Loss Expectancy (ALE), and mitigation ROI lab
- Tiered volume discounting, wholesale price breaks, and margin elasticity lab
- Warehouse storage capacity, pallet cube utilization, and picking velocity lab
- Call center Erlang C queuing, SLA service levels, and shrinkage staffing lab
- TAM, SAM, SOM market sizing, bottom-up account volumes, and revenue penetration lab
- Retail Open-To-Buy (OTB), markdown optimization, and inventory sell-through lab
- Hotel revenue management, RevPAR, ADR, GOPPAR, and CompSet yield lab
- Critical Path Method (CPM), PERT expected duration, and schedule variance lab
- Professional services billable utilization, billing realization, and rate lab
- Price elasticity of demand (PED), arc elasticity, and revenue maximization lab
- BCG Growth-Share Matrix, Relative Market Share (RMS), and portfolio capital allocation lab
- A/B testing sample size, two-proportion Z-score statistical significance, and conversion lift lab
- Economic Production Quantity (EPQ), finite run length, and setup vs holding cost lab
- Retail Sell-Through Rate (STR), Weeks of Supply (WOS), and markdown timing lab
- Porter's Five Forces, industry attractiveness, and competitive strategy lab
- Van Westendorp Price Sensitivity Meter (PSM), willingness to pay, and acceptable price lab
- Customer Lifetime Value (CLV / LTV), CAC payback, and customer equity lab
- Value at Risk (VaR), Expected Shortfall (CVaR), and portfolio tail risk lab
- Little's Law, Work in Process (WIP), cycle time, and Lean flow lab
- SWOT analysis, TOWS action matrix, and strategic formulation lab
- Markup vs. Margin, gross profit, selling price, and discount breakeven lab
- Employee Absenteeism, Bradford Factor, overtime replacement, and workforce drag lab
- Net Promoter Score (NPS), CSAT, Detractor churn drag, and customer retention ROI lab
- Business Continuity, Maximum Tolerable Downtime (MTD), RTO, RPO, and outage cost lab
- Value Stream Mapping (VSM), Lead Time, Process Cycle Efficiency (PCE), and Rolled Yield lab
- Ansoff Growth Matrix, market penetration vs diversification risk, and EMV valuation lab
- RFM customer segmentation, cohort reactivation conversion, and campaign marketing ROI lab
- Labor productivity, Revenue per Employee (RPE), Labor Cost Ratio (LCR), and EBIT gain lab
- Bundle pricing, mixed bundling, product cannibalization, and profit lift lab
- Six Sigma DMAIC process sigma level, DPMO, First Pass Yield, and COPQ savings lab
- VRIO framework, Resource-Based View (RBV), and sustained competitive advantage lab
- Agency client profitability, direct gross margin, fully allocated net margin, and concentration risk lab
- Marketing multi-touch attribution (MTA), media mix modeling (MMM), and channel ROAS lab
- Failure Mode and Effects Analysis (FMEA), Risk Priority Number (RPN), and Action Priority lab
- Dynamic peak pricing, demand surge multipliers, price elasticity, and capacity yield lab
- Statistical quality control (SQC), Acceptance Quality Limit (AQL), OC curve, and AOQL lab
- Retail markdown optimization, clearance cadences, gross margin dilution, and terminal salvage lab
- Compensation compa-ratio, salary range penetration, range spread, and merit increase lab
- Viral coefficient (K-factor), viral cycle time, organic amplification, and compounding growth lab
- Weighted Average Cost of Capital (WACC), CAPM cost of equity, after-tax debt, and hurdle rate lab
- Cash runway, gross and net burn rate, Zero Cash Date (ZCD), and Default Alive trajectory lab
- Monte Carlo simulation, probabilistic DCF, expected NPV, loss probability, and Value at Risk lab
- Supply chain Bullwhip Effect, multi-echelon demand distortion, and order variance amplification lab
- Theory of Constraints (TOC), bottleneck exploitation, Drum-Buffer-Rope, and Throughput Accounting lab
- Cohort retention decay curves, power-law vs exponential churn, Net Revenue Retention (NRR), and LTV lab
- Price skimming vs market penetration strategy, consumer surplus, R&D payback, and market share lab
- Span of control ratios, management layers, organizational overhead costs, and Graicunas complexity lab
- Altman Z-Score bankruptcy prediction, financial distress zones, and insolvency risk lab
- Capital Asset Pricing Model (CAPM), equity risk premium, levered vs unlevered beta, and Jensen's alpha lab
- Total Cost of Ownership (TCO), landed supplier sourcing costs, pipeline inventory, and tariffs lab
- Customer Acquisition Cost (CAC) by channel, blended CAC, channel LTV:CAC, and payback lab
- Service Level Agreement (SLA), the nines uptime, MTTR/MTBF, and downtime financial cost lab
- Two-part tariff pricing, fixed access fees, variable usage rates, and consumer surplus extraction lab
- Newsvendor model, single-period inventory optimization, critical fractile service level, and EVPI lab
- Leveraged Buyout (LBO), 5-year debt paydown schedules, sponsor IRR, MOIC, and returns attribution lab
- Menu engineering, Kasavana-Smith profitability matrix, item contribution margins, and food cost % lab
- Consulting leverage ratios, staff pyramid economics, David Maister 3-factor formula, and Profit Per Partner lab
- Credit risk, Expected Loss (PD x LGD x EAD), Unexpected Loss economic capital, and Basel RAROC lab
- Target costing, market allowable cost, Value Engineering (VE) teardowns, and Value Index matrix lab
- Dividend Discount Model (DDM), Gordon Growth, Two-Stage DDM, and H-Model equity valuation lab
- Single-Minute Exchange of Die (SMED), quick changeovers, internal vs external setup, and batch size lab
- Economic Value Added (EVA), ROIC-WACC economic spread, NOPAT, and MVA wealth creation lab
- Overtime vs. new hire staffing, 1.5x wage premiums, benefits burden, and breakeven capacity lab
- Restaurant prime cost, Food & Beverage COGS, labor cost benchmarks, and menu price uplift lab
- ABC-XYZ inventory classification, Pareto 80/20 annual usage value, demand volatility CV, and matrix replenishment lab
- Retainer vs. Time & Materials (T&M) vs. Fixed-Fee profitability, scope creep, and Effective Hourly Rate (EHR) lab
- Degree of Operating Leverage (DOL), fixed vs. variable cost structure, and EBIT volatility magnification lab
- Standard costing, Direct Material & Labor variances (MPV, MQV, LRV, LEV), and overhead volume absorption lab
- Labor burden rate, statutory payroll taxes, health insurance, 401(k) match, PTO downtime, and realized productive billable rate lab
- Restaurant RevPASH, table turnover velocity, seat occupancy %, and average check yield lab
- Supply chain disruption, Time-to-Recover (TTR), Time-to-Survive (TTS), and Risk Exposure Index (REI) lab
- Bond duration, Macaulay & Modified duration, Convexity adjustments, and DV01 interest rate risk lab
- Strategic real options valuation, Black-Scholes managerial flexibility, option to expand, and expanded NPV lab
- Professional services realization rate, billing write-downs, collection write-offs, and Effective Hourly Rate (EHR) lab
- Debt service coverage ratio (DSCR), fixed charge coverage (FCCR), maximum loan capacity, and debt yield lab
- Equipment reliability, MTBF, MTTR, operational availability, downtime financial losses, and preventive maintenance ROI lab
- Business interruption insurance, Actual Loss Sustained (ALS), continuing fixed overhead, coinsurance, and extra expense lab
- Value-based pricing, Economic Value to the Customer (EVC), competitor reference value, and customer surplus sharing lab
- Lead scoring, firmographic fit, behavioral intent, MQL-to-SQL qualification, and sales pipeline velocity lab
- Post-merger integration (PMI), cost/revenue synergy phasing, Costs to Achieve (CTA), and deal value creation lab
- Employee lifetime value (ELTV), onboarding ramp velocity, burdened payroll, peak productivity, and talent ROI lab
- Commercial lease, triple net (NNN) CAM expenses, natural breakpoints, percentage rent overage, and occupancy cost ratio lab
- Manufacturing learning curve, Wright's Law, progress ratios, N-th unit direct labor, and batch pricing lab
- Net dollar retention (NDR / NRR), gross retention (GRR), churn/contraction leakage, and SaaS cohort waterfall lab
- Sustainable growth rate (SGR), internal growth rate (IGR), DuPont ROE, and corporate self-financing lab
- Freemium conversion, cost per free user, breakeven conversion, and product-led growth (PLG) pricing lab
- Retail inventory shrinkage, loss prevention (LP) ROI, and phantom stockout discrepancy lab
- Billing rate multiplier, direct labor burden, overhead (OH/DL), and consulting rate card lab
- Sales quota, tiered commission accelerators, OTE pay mix, and sales rep cash compensation lab
- Hotel GOPPAR, TrevPAR, RevPAR, and lodging gross operating profit flow-through lab
- Debt-to-equity (D/E), financial leverage, interest coverage (TIE), and Hamada beta lab
- Rolled throughput yield (RTY), first pass yield (FPY), hidden factory rework, and defect cascade lab
- Effective hourly rate (EHR), scope creep hour dilution, fixed-fee realization, and loaded cost margin lab
- Average spend per cover (ASPC), guest check average, F&B sales mix, and restaurant prime cost lab
- Franchise ROI, initial investment payback, royalty fee drag, and store EBITDA unit economics lab
- Marketing Efficiency Ratio (MER), blended ROAS, new customer CAC, and contribution profit lab
- Assembly line balancing efficiency, takt time, theoretical minimum workstations, and balance delay lab
- Accounts receivable aging, Days Sales Outstanding (DSO), bad debt allowance, and cash acceleration lab
- Earned Value Management (EVM), CPI, SPI, Cost/Schedule Variances, and EAC forecast lab
- Customer concentration risk, Herfindahl-Hirschman Index (HHI), and M&A multiple discount lab
- Cross-Price Elasticity of Demand (XED), substitutes, complements, and cannibalization lab
- Human Capital ROI (HCROI), Human Capital Value Added (HCVA) per FTE, and labor leverage lab
- Hotel OTA commission, Net ADR yield, channel distribution mix, and direct shift profit lab
- Enterprise Value (EV) to Equity Value bridge, Net Debt, and M&A waterfall lab
- Black-Scholes European option pricing, Greeks (Delta/Gamma/Theta/Vega/Rho), and volatility lab
- Queuing theory (M/M/s waiting lines), Erlang C delay probability, and staffing cost lab
- Sales Per Square Foot (SPSF), Gross Margin Return on Space (GMROS), and retail lease lab
- Share of Voice (SOV), Excess Share of Voice (ESOV), and market share growth lab
- Accounts payable (DPO), trade credit discount APR (2/10 Net 30), and cash unlock lab
- Risk-Adjusted Return on Capital (RAROC), economic capital, and SVA lab
- Hotel RevPAR Index (RGI), Market Penetration (MPI), Average Rate Index (ARI), and fair share lab
- Return on Invested Capital (ROIC), NOPAT, and economic spread lab
- FTE & workforce capacity planning, shrinkage %, and staffing lab
- Initial Markup (IMU), Maintained Markup (MMU), and retail reductions lab
- FX hedging, currency transaction risk, forward rates, and VaR lab
- Advertising adstock, media saturation, half-life, and marginal ROAS lab
- Hotel flow-through %, operating flex %, and GOP conversion lab
- Discounted payback period, nominal payback, NPV, and capital recovery lab
- Levered and unlevered beta, Hamada equation, peer comps, and cost of equity lab
- Free cash flow to firm (FCFF) vs. equity (FCFE), DCF bridges, and NWC reinvestment lab
- Price break EOQ, quantity discount tiers, holding vs. purchase savings, and order policy lab
- Yield to maturity (YTM), bond pricing, current yield, and Newton-Raphson iteration lab
- Credit spread, G-spread over Treasuries, implied default probability, and hazard rate lab
- Kanban card sizing, CONWIP WIP limits, Little's Law lead time, and inventory carrying cost lab
- Sharpe ratio, Sortino downside deviation, Treynor systematic risk, and Jensen's alpha lab
- Cash Conversion Efficiency (CCE % = FCF ÷ Revenue), Operating Cash Flow margin, CapEx intensity, and earnings quality realization lab
- Statement of Retained Earnings (Beginning + Net Income - Dividends), plowback retention rates, and Higgins Sustainable Growth Rate lab
- Cost of Equity (Ke), CAPM, Gordon Growth Model, Bond Yield Plus Risk Premium triangulation, and hurdle rate lab
- Net Operating Profit After Tax (NOPAT = EBIT × (1 - t)), invested capital charge, and Economic Value Added (EVA) lab
- Earnings Yield (E/P), inverse P/E ratio, Fed Model equity risk premium spread over 10-year Treasuries, and real yield lab
- Equity Risk Premium (ERP), Historical, Damodaran Implied Forward DCF, and Ibbotson-Chen supply-side model lab
- Dividend Coverage Ratio (DCR = EPS ÷ DPS), Free Cash Flow coverage, payout headroom, and dividend safety lab
- Working Capital Funding Gap (AR + Inventory - AP), Cash Conversion Cycle days, revolving credit line requirements, and growth deficit lab
- Working Capital Turnover ratio, Days Working Capital (DWC), capital support capacity, and overtrading risk lab
- Net working capital (NWC), operating working capital (OWC), liquidity ratios, and cash unlock lab
- SaaS magic number, sales efficiency, net new ARR, and CAC payback period lab
- Interest rate swap (IRS) valuation, fixed vs. floating leg cash flows, swap rate solver, and DV01 hedge lab
- SaaS Rule of 40, revenue growth vs. FCF margin, valuation multiple expansion, and Bessemer benchmark lab
- Burn Multiple, startup capital efficiency, net burn vs. net new ARR, and runway lab
- SaaS Quick Ratio, subscription revenue waterfall, net new ARR dynamics, and churn drag lab
- Internal rate of return (IRR), modified IRR (MIRR), NPV profiles, and capital budgeting lab
- Terminal value (TV), Gordon growth perpetuity, exit multiples (EV/EBITDA), and DCF enterprise valuation lab
- Reorder point (ROP), statistical safety stock, lead-time and demand variance, and cycle service level lab
- Discounted cash flow (DCF) model, unlevered free cash flows, WACC discounting, terminal value, and equity bridge lab
- LTV:CAC ratio, discounted customer lifetime value, CAC payback period, and unit economics lab
- Startup cash runway, Zero Cash Date (ZCD), monthly net burn, revenue ramp, and fundraising buffer lab
- Debt service coverage ratio (DSCR), commercial real estate underwriting, max supportable loan, and debt yield lab
- Target return on investment (ROI) pricing, full absorption unit cost, required operating profit markup, and breakeven volume lab
- Inventory stockout cost, lost sales margin, backorder expediting, customer churn drag, and optimal service level (CSL*) lab
- Nurse-to-patient ratio, nursing hours per patient day (HPPD), shift scheduling, core vs. agency mix, and clinical safety lab
- Free cash flow (FCF), operating cash flow (OCF), CapEx reinvestment, FCFF, FCFE, and cash conversion lab
- Sales velocity, daily pipeline revenue, win rate, deal size, and cycle compression acceleration lab
- Piotroski F-Score, 9-point fundamental accounting criteria, earnings quality, and bankruptcy screening lab
- Beneish M-Score, 8-variable earnings manipulation detection, probability of manipulation, and forensic accounting lab
- Email marketing ROI, subscriber list decay, revenue per recipient (RPR), deliverability, and conversion waterfall lab
- CPM, CPC, click-through rate (CTR), cost per acquisition (CPA), conversion rate, ROAS, and ad arbitrage lab
- Contribution margin, contribution margin ratio (CMR), break-even units and revenue, margin of safety, and CVP operating leverage lab
- Operating cycle, gross cash velocity, Days Inventory Outstanding (DIO), Days Sales Outstanding (DSO), and working capital carrying drag lab
- Compound Annual Growth Rate (CAGR), geometric multi-year expansion, inflation-adjusted real CAGR, Rule of 72 doubling, and target valuation lab
- SaaS ARR waterfall, Net Revenue Retention (NRR), Gross Revenue Retention (GRR), expansion, contraction, and cohort bridge lab
- Quick Ratio (Acid-Test), Cash Ratio, liquid working capital buffer, short-term debt coverage, and solvency lab
- Capitalization rate (Cap Rate), commercial real estate valuation, Net Operating Income (NOI), Effective Gross Income (EGI), and exit cap spread lab
- Adjusted EBITDA, Quality of Earnings (QoE), M&A add-back reconciliation, EV/EBITDA buyout multiples, and pro-forma run-rate lab
- Net Debt to EBITDA, gross leverage, lending covenant headroom, and debt de-leveraging lab
- Times Interest Earned (TIE), EBITDA interest coverage, cash interest coverage, debt capacity, and covenant solvency lab
- Gross margin %, markup on cost, cost of goods sold (COGS), volume break-even, and pricing optimization lab
- Total Asset Turnover (TAT), Fixed Asset Turnover (FAT), Working Capital Velocity, and DuPont ROE lab
- Current ratio, Acid-Test Quick Ratio, Cash Ratio, Net Working Capital buffer, and covenant liquidity lab
- Operating Profit Margin (EBIT Margin), SG&A overhead drag, OPEX ratio, and operating leverage lab
- Fixed Charge Coverage Ratio (FCCR), operating leases, debt principal amortization, and commercial covenant lab
- Operating Cash Flow Ratio (OCF Ratio), Cash Flow from Operations (CFO), short-term debt coverage, and liquidity lab
- Gross Margin Return on Inventory Investment (GMROI), inventory turnover, markup on cost, and holding cost lab
- Return on Capital Employed (ROCE), Capital Employed, EBIT margin, capital turnover, and economic spread lab
- Days Sales Outstanding (DSO), Accounts Receivable Turnover, collections cash velocity, and liquidity unlock lab
- Days Payables Outstanding (DPO), Accounts Payable Turnover, trade credit financing, and early discount APR lab
- Days Inventory Outstanding (DIO), Days Sales of Inventory (DSI), inventory carrying cost drag, and working capital cash unlock lab
- Return on Assets (ROA), DuPont asset turnover decomposition, unlevered operating returns, and capital productivity lab
- Sortino Ratio, downside semi-deviation, MAR hurdle excess return, and Sharpe Ratio asymmetry lab
- Price-to-Earnings (P/E) Ratio, Peter Lynch PEG Ratio, earnings yield, equity risk premium, and implied fair value equity valuation lab
- Treynor Ratio, CAPM systematic risk beta, market risk premium, and diversified portfolio performance lab
- Calmar Ratio, maximum drawdown (MDD), Sterling Ratio, and tail-risk recovery resilience lab
- Price-to-Book (P/B) Ratio, Tangible Book Value per share, justified ROE-driven P/B, and equity valuation lab
- Price-to-Sales (P/S) Ratio, EV/Sales multiples, margin-justified revenue multiples, and equity valuation lab
- Enterprise Value-to-EBITDA (EV/EBITDA), capital structure bridge, and valuation multiples lab
- Enterprise Value-to-EBIT (EV/EBIT) Ratio, Operating Earnings Yield (EBIT/EV), capital intensity adjustment, and valuation multiples lab
- Enterprise Value-to-Sales (EV/Sales) multiple, net debt capital structure adjustments, and revenue valuation lab
- EBIT margin, operating profit waterfall, SG&A overhead drag, and degree of operating leverage (DOL) lab
- Net Profit Margin %, complete top-to-bottom income statement waterfall, interest and tax burdens, and EPS lab
- EBITDA margin %, operating cash profitability, D&A capital intensity drag, and EBITDA-to-EBIT conversion lab
- Free Cash Flow (FCF) margin %, Operating Cash Flow (OCF) conversion, CapEx intensity drag, and earnings cash quality lab
- Operating Cash Flow (OCF) margin %, Cash Flow from Operations (CFO) waterfall, working capital drag, and cash quality lab
- Sloan Ratio, accrual anomaly, earnings quality, balance sheet vs. cash flow accruals, and restatement risk lab
- Dividend Discount Model (DDM), Gordon Constant Growth, Two-Stage supernormal expansion, Fuller-Hsia H-Model, and intrinsic equity valuation lab
- Price-to-Cash-Flow (P/CF) Ratio, Price-to-Free-Cash-Flow (P/FCF), cash flow yield, and equity valuation lab
- Free Cash Flow (FCF) Yield, cash per share, dividend safety coverage, and cash allocation lab
- Dividend yield, EPS and FCF payout ratios, yield on cost (YOC), and dividend sustainability lab
- Dividend Payout Ratio, GAAP EPS vs. FCF payout, plowback retention rate, and distribution safety lab
- Plowback Ratio, retention rate, Sustainable Growth Rate (SGR), DuPont ROE, and equity reinvestment lab
- Reinvestment Rate, net capital expenditures, change in working capital, ROIC, and fundamental operating growth lab
- Omega Ratio, probability-weighted gain/loss expectancy, threshold return hurdle, and asymmetric payoff lab
- Graham Number, Benjamin Graham 22.5 rule, margin of safety %, Net Current Asset Value (NCAV), and deep value lab
- Internal Growth Rate (IGR), zero-debt self-funded expansion, External Financing Needed (EFN), and Higgins SGR contrast lab
- Market Value Added (MVA = Enterprise Market Value - Invested Capital), single-period EVA, and shareholder wealth creation lab
- Residual Income Valuation (Edwards-Bell-Ohlson), equity charges, Clean Surplus Accounting, persistence decay, and justified P/B lab
- Adjusted Present Value (APV), unlevered DCF, interest tax shields, dynamic debt paydown, and distress cost lab
- Fuller-Hsia H-Model, linear growth fade, terminal perpetuity, implied cost of equity, and discrete DCF cash flow schedule lab
- Asian option pricing (arithmetic & geometric average), Kemna-Vorst closed forms, Turnbull-Wakeman moment matching, and volatility dampening lab
- Lookback option pricing (floating & fixed strike), Goldman-Sosin-Gatto and Conze-Viswanathan closed forms, Broadie-Glasserman-Kou discrete monitoring, and extrema Greeks lab
- Margrabe exchange option pricing, two-asset Black-Scholes framework, combined spread volatility, cross-asset Greeks, and spark spread valuation lab
- Compound option pricing (Geske 1979), options on options (CoC, PoC, CoP, PoP), critical boundary S*, bivariate normal integrals, and staged real options lab
- Chooser option pricing (Rubinstein 1991), as-you-like-it options, choice date flexibility, critical price boundary S*, and straddle discount lab
- Bermudan option pricing, discrete exercise schedules, CRR recombining binomial lattices, early exercise boundaries, and American vs European premiums lab
- Forward start option pricing (Rubinstein 1991), future strike determination date t1, moneyness multiple alpha, cliquet notes, and pre-start Greeks lab
- Gap option pricing, dual strike hurdles (K1 trigger, K2 payoff), negative option values, jump discontinuities, and Greeks cliff lab
- Rainbow option pricing (Johnson 1987), two-asset best-of and worst-of payoff structures, bivariate normal distributions, cross-asset correlation risk, and Greeks lab
- Basket option pricing, arithmetic weighted portfolio moment matching, Ju (2002) approximations, diversification discount, and component Greeks lab
- Digital option pricing, cash-or-nothing and asset-or-nothing binaries, extreme pin risk, Dirac delta Greeks, and tight call spread static replication lab
- Quanto option pricing, cross-currency fixed exchange rate guarantees, Girsanov drift adjustments (-rho*sigma_S*sigma_X), and correlation risk lab
- Power option pricing, non-linear payoffs (S_T^alpha - K), Itô volatility magnification (alpha*sigma), super-convexity, and higher-order Greeks lab
- Cliquet option pricing, periodic strike reset ratchets, local return caps & floors, forward-start option series decomposition, and equity structured notes lab
- Variance swap pricing, Demeterfi et al. (1999) log-contract replication strips (1/K²), fair variance strikes, vega notionals, and volatility convexity lab
- Autocallable structured note pricing, Phoenix memory coupons, early redemption trigger schedules, downside knock-in put protection, and expected duration lab
- Credit Default Swap (CDS) pricing, ISDA standard coupons (100/500 bps), upfront settlement points, hazard rate bootstrapping, survival curves Q(t), and CS01/DV01 hedge ratios lab
- Credit Valuation Adjustment (CVA), Debit DVA, Bilateral BCVA, Expected Positive Exposure (EE/EPE), Potential Future Exposure (PFE 95th/99th), and ISDA CSA collateral netting lab
- Forward Rate Agreement (FRA) pricing, AxB money market conventions, implied no-arbitrage forward rate bootstrapping, in-advance discounted cash settlements, and borrower/lender hedging lab
- Interest rate cap, floor & collar pricing, Black-76 caplet strips, zero-cost collar structuring, cap-floor parity, and Vega/Theta risk management lab
- European swaption pricing, Black-76 lognormal vs. Bachelier normal models, Expiry × Tenor volatility grids, swap annuity PVBP, and payer/receiver Greeks lab
- Constant Maturity Swap (CMS) pricing, numeraire change convexity adjustments, swap annuity function G(y), CMS caps/floors, and curve steepener spread options lab
- Bermudan swaption pricing, 1-factor Hull-White trinomial lattice dynamic programming, optimal exercise stopping boundaries r*(t), and early exercise premium lab
- Corporate debt restructuring, creditor haircuts, debt-to-equity swaps (DES), post-recapitalization equity value, existing shareholder dilution, and debt service covenant restoration lab
- Convertible bond pricing, conversion parity (CR × S), straight debt investment floor, embedded option premium, conversion premium, and convertible arbitrage delta hedging lab
- Bond convexity, analytical second derivative curvature, Macaulay vs. modified duration, dollar convexity, and second-order Taylor series price shock approximation lab
- Barbell vs. bullet bond portfolio strategies, duration matching, barbell convexity advantage, yield giveup drag, and yield curve reshaping/butterfly shifts lab
- Key rate duration (KRD) vector decomposition, Ho (1992) tent functions, non-parallel curve twists, effective duration sum-check, and portfolio shaping risk lab
- Spot vs. forward rate curve bootstrapping, par yield recursive decomposition, implied forward metrics (1y1y, 2y3y, 5y5y), and term premium dynamics lab
- Nelson-Siegel & Svensson parametric yield curve fitting, Level, Slope, and Curvature factor decomposition, instantaneous forward curves, and RMSE calibration lab
- Z-spread (Zero-Volatility Spread) numerical spot curve inversion, Option-Adjusted Spread (OAS) in callable/putable bonds, and Par-Par Asset Swap Spread (ASW) lab
- European box spread arbitrage, Put-Call Parity synthetic replication, implied borrowing/lending interest rate yields, and American early assignment risk lab
- Iron Condor options income strategies, Probability of Profit (POP) lognormal diffusion, risk-reward ratios, dual breakevens, and portfolio Greeks curve evolution lab
- Butterfly spread options structures (1-2-1), Black-Scholes Greeks, asymmetric broken-wing variations, pin risk, and time-decay theta acceleration lab
- Straddle and strangle pure volatility strategies, market-implied expected move rule (0.85 × Straddle), post-earnings IV crush, and dual breakevens lab
- Calendar and diagonal spread time options, non-linear theta divergence (1/√T), IV term structure skew, and front expiry payoffs lab
- Ratio spread (1:2) and volume backspread (2:1) options mechanics, asymmetric tail risk, naked strike breakevens, and Black-Scholes Greeks lab
- Condor spread (Long & Short) 4-strike options strategies, flat profit plateau (K2-K3), dual breakevens, and Black-Scholes Greeks lab
- Seagull spread (Bull & Bear) 3-strike options hedging, zero-cost corridors, asymmetric tail risk, and Black-Scholes Greeks lab
- Collar strategy (Zero-Cost & Protective) options hedging, floor/ceiling corridors, portfolio Greek stabilization, and Black-Scholes pricing lab
- Strip and strap asymmetric options structures, directional volatility leverage (2:1 put/call ratios), asymmetric breakevens, and Greeks lab
- Iron Butterfly 4-leg credit options structures, short ATM straddle core, defined OTM wings, peak profit apex, and Black-Scholes Greeks lab
- Christmas Tree spread (1-2-3 & 1-1-2) asymmetric option ladders, low net debit entry, directional bias with defined risk, and Greeks lab
- Risk Reversal & volatility skew strategies, FX 25-delta skew arbitrage, zero-cost synthetic long/short setups, and Black-Scholes Greeks lab
- Jelly Roll options arbitrage, calendar synthetic loan pricing, put-call parity theoretical valuation, implied financing rates, and assignment risk lab
- Dispersion trading volatility arbitrage, index vs. basket straddles, implied correlation solving, vega-neutral hedging, and correlation risk premium (CRP) lab
- Synthetic futures and synthetic stock options strategies, Put-Call Parity replication (+C/-P), cost of carry forward pricing, and zero-vega Greeks lab
- Breeden-Litzenberger (1978) model-free risk-neutral density extraction, second derivative curvature q(K), butterfly replication, and skewness/kurtosis lab
- Vanna-Volga pricing and 2nd-order Greek hedging, 3-pillar calibration portfolio (ATM, 25-delta RR, 25-delta BF), cross-gamma risk, and implied volatility smile reconstruction lab
- 3D implied volatility surface geometry and Gatheral (2004) SVI calibration, cross-sectional strike skews, term structure contango/backwardation, and calendar/butterfly no-arbitrage bounds lab
- Institutional volatility cones (Burghardt & Lane 1990), multi-horizon realized volatility percentiles (10-252d), estimator efficiencies (Parkinson, Garman-Klass, Yang-Zhang), and Volatility Risk Premium (VRP) lab
- Two-asset spread option pricing via Kirk's (1995) approximation, Margrabe zero-strike limit, cross-asset Greeks, commodity crack/spark spreads, and correlation sensitivity lab
- Bruno Dupire (1994) local volatility surface extraction from implied variance w(k,T), continuous diffusion, 2x slope rule of thumb, calendar/butterfly no-arbitrage bounds, and forward smile lab
- CBOE Volatility Index (VIX) calculation formula, log contract replication with 1/K² weights, zero-bid truncation, and 30-day term roll interpolation lab
- Volatility swap pricing, Jensen's inequality convexity drag (K_vol < √K_var), Brockhaus-Long analytical Taylor approximation, and linear vs. variance payoffs lab
- Correlation swap pricing, Sebastien Bossu (2005) index vs constituent variance decomposition, Correlation Risk Premium (CRP), systemic contagion, and mark-to-market blending lab
- Corridor variance swap pricing, Peter Carr & Roger Lee (2007) bounded 2/K² replication strips, downside semi-variance crash hedging, barrier pin risk, and conditional accrual lab
- Forward Volatility Agreement (FVA) pricing, forward starting variance swaps, calendar variance replication (+T2/-T1), forward convexity drag, and term structure roll-down carry lab
- VIX futures and options pricing, risk-neutral mean reversion (kappa/theta), term structure roll yield carry, Black-76 options with positive skew, and ETP drag lab
- Constant Proportion Portfolio Insurance (CPPI), Black & Jones (1987) dynamic floor protection, cushion multiplier, cash-lock trap, and gap crash risk lab
- Option-Based Portfolio Insurance (OBPI), Leland & Rubinstein (1976) protective puts, 90/10 capital protected notes, equity participation rates, and Black-Scholes theta decay lab
- Time-Invariant Portfolio Protection (TIPP), Estep & Kritzman (1988) ratcheted trailing floors, high-water mark tracking, perpetual investment horizon, and cash-lock trade-offs lab
- Risk Parity & Equal Risk Contribution (ERC), Maillard, Roncalli & Teïletche (2010), Qian (2005) covariance risk budgeting, 60/40 risk illusions, and All-Weather diversification lab
- Hierarchical Risk Parity (HRP), Marcos López de Prado (2016) machine learning portfolio allocation, single-linkage tree clustering, quasi-diagonalization, and recursive bisection lab
- Maximum Diversification Portfolio (MDP), Yves Choueifaty & Yves Coignard (2008) Diversification Ratio (DR) optimization, equi-correlation property, and diversification alpha lab
- Resampled Efficient Frontier, Richard & Robert Michaud (1998) Monte Carlo parameter uncertainty, bootstrap resampling, transition mapping, and out-of-sample stability lab
- Ledoit-Wolf Covariance Shrinkage & Random Matrix Theory, Olivier Ledoit & Michael Wolf (2004) optimal linear shrinkage ($\Sigma^* = \delta F + (1-\delta)S$), Marcenko-Pastur spectral noise bounds, and condition number stabilization lab
- Kelly Criterion Multi-Asset Portfolio, John L. Kelly Jr. (1956), Edward Thorp (1969) logarithmic capital growth, multivariate leverage ($w^* = \Sigma^{-1}(\mu - r_f\mathbf{1})$), Half-Kelly variance reduction, and drawdown probability lab
- Fundamental Law of Active Management, Richard Grinold (1989), Ronald Kahn (2000), Clarke, de Silva & Thorley (2002) Information Ratio ($\text{IR} = TC \times \text{IC} \times \sqrt{BR^*}$), transfer coefficient, breadth compression, and active alpha lab
- Brinson Portfolio Performance Attribution, Gary Brinson, Randolph Hood & Gilbert Beebower (BHB 1986), Brinson & Nimrod Fachler (BF 1985) Sector Allocation, Security Selection, Interaction effects, and Carino multi-period linking lab
- Barra Multi-Factor Risk Model, Barr Rosenberg (1974), Stephen Ross (1976) Arbitrage Pricing Theory, systematic factor covariance ($\mathbf{X}\mathbf{F}\mathbf{X}^T$), idiosyncratic specific risk ($\boldsymbol{\Delta}$), and active tracking error budgeting lab
- Almgren-Chriss (2000) Optimal Execution, Robert Almgren & Neil Chriss market impact theory, permanent vs. temporary impact, optimal hyperbolic liquidation trajectories ($x(t)$), variance of capture, and execution efficient frontier lab
- Sharpe (1988, 1992) Returns-Based Style Analysis (RBSA), William F. Sharpe constrained quadratic programming, effective asset allocation, $R^2$ style fit, active selection alpha, and rolling style drift index (SDI) lab
- Copula & Tail Dependence Portfolio Risk, Sklar's Theorem (1959), Gaussian, Student-t, Clayton, and Gumbel copulas, lower and upper tail dependence ($\lambda_L, \lambda_U$), joint default probability, and systemic crash contagion lab
- Conditional Value-at-Risk (CVaR) & Expected Shortfall Optimization, R. Tyrrell Rockafellar & Stanislav Uryasev (2000) linear programming formulation, Euler component tail risk decomposition, and Basel III / FRTB capital adequacy lab
- GARCH(1,1) & GJR-GARCH Volatility Forecasting, Tim Bollerslev (1986), Robert Engle (1982) autoregressive conditional heteroskedasticity, volatility clustering, shock persistence, half-life, news impact curves, and term structure forecasting lab
- Variance Gamma (VG) Option Pricing, Dilip B. Madan, Peter P. Carr & Eric C. Chang (1998) pure jump Lévy process, stochastic operational time subordination, leptokurtic return density, volatility smile/skew, and Fourier inversion lab
- Kou Jump-Diffusion Option Pricing, Steven G. Kou (2002) double exponential jump-diffusion model, asymmetric jump decays ($\eta_1, \eta_2$), memoryless property, jump compensator ($\zeta$), and Fourier inversion smile lab
- Bates (1996) Stochastic Volatility Jump-Diffusion, David S. Bates unified Heston CIR continuous variance with Merton compound Poisson lognormal jumps, jump compensator ($\bar{k}$), Fourier inversion, and volatility smile lab
- Constant Elasticity of Variance (CEV) Option Pricing, John C. Cox (1975) local volatility diffusion ($dS = \mu S dt + \sigma S^\beta dW$), elasticity of variance ($2(\beta - 1)$), non-central chi-square analytical pricing, absorbing default barrier, and leverage skew lab
- Merton (1969, 1971) Continuous-Time Portfolio Choice & Optimal Consumption, Robert C. Merton Hamilton-Jacobi-Bellman (HJB) stochastic control, CRRA power utility, optimal risky asset share ($\alpha^* = \frac{\mu - r}{\gamma \sigma^2}$), dynamic spending propensity ($\nu(t)$), and longevity ruin analysis lab
- Carr-Madan (2001) Static Option Replication & Model-Free Volatility, Peter Carr & Dilip Madan static spanning theorem, exact Taylor payoff expansion, VIX log contract replication, discrete strike mesh weighting ($w_i = F''(K_i)\Delta K$), and synthetic Greeks lab
- Kyle's Lambda & Market Microstructure, Pete Kyle (1985) insider trading equilibrium, order flow price impact ($\lambda = \frac{\sigma_v}{2\sigma_u}$), market depth ($D = 1/\lambda$), Glosten-Milgrom (1985) sequential Bayesian adverse selection spread, Roll (1984) effective spread, and Amihud illiquidity lab
- Pairs Trading & Statistical Arbitrage, Marco Avellaneda and Jeong-Hyun Lee (2010) Ornstein-Uhlenbeck spread model ($dX_t = \kappa(\theta - X_t)dt + \sigma dW_t$), Engle-Granger cointegration, dimensionless $s$-score trading rules, mean-reversion half-life ($t_{1/2} = \frac{\ln(2)}{\kappa}$), and market-neutral backtest lab
- Volume-Synchronized Probability of Toxicity (VPIN), David Easley, Marcos López de Prado, and Maureen O'Hara (2012) flow toxicity, volume clock discretization ($V = \text{ADV}/N_{\text{buckets}}$), Bulk Volume Classification (BVC, $V_\tau^B = V \cdot \Phi(\Delta P / \sigma_{\Delta P})$), toxicity CDF warning thresholds ($F_{\text{VPIN}} \ge 0.99$), and flash crash liquidity cascade lab
- Avellaneda-Stoikov (2008) High-Frequency Market Making, Marco Avellaneda & Sasha Stoikov reservation price ($r = s - q\gamma\sigma^2(T-t)$), optimal bid-ask quoting schedule ($p^a, p^b$), inventory risk penalty, order book liquidity decay ($\kappa$), and inventory mean-reversion lab
- Hasbrouck (1995) Information Share & Gonzalo-Granger (1995) Component Share, Vector Error Correction Model (VECM), cointegration, Cholesky factorization bounds ($[IS^{\min}, IS^{\max}]$), price leadership attribution, and cross-market innovation correlation lab
- Huang & Stoll (1997) Bid-Ask Spread Decomposition, structural econometric trade indicator model, adverse selection ($\alpha$), inventory holding cost ($\beta$), order processing profit ($\gamma$), flow persistence ($\pi$), and realized spread decay lab
- Yang-Zhang (2000) & Range-Based Volatility, Dennis Yang & Qiang Zhang minimum-variance unbiased estimator ($\sigma_{YZ}^2 = \sigma_o^2 + k\sigma_c^2 + (1-k)\sigma_{RS}^2$), Parkinson (1980), Garman-Klass (1980), Rogers-Satchell (1991) drift independence, and statistical efficiency gains lab
- Madhavan-Richardson-Roompack (1997) MRR Spread Decomposition, structural price determination model, trade surprises ($\xi_t = x_t - \rho x_{t-1}$), adverse selection ($\alpha$), order processing ($\phi$), serial correlation ($\rho$), public news shock ($\sigma_u^2$), and return variance attribution lab
- Barndorff-Nielsen & Shephard (2004, 2006) Realized Bipower Variation ($BV = \frac{\pi}{2} \sum |r_j||r_{j-1}|$), continuous vs jump variance disentanglement ($JV = \max[RV - BV, 0]$), Tri-power Quarticity ($TQ$), and BNS non-parametric jump test lab
- Cont-Kukanov-Stoikov (2014) Order Flow Imbalance (OFI) & Price Impact, limit order book event decomposition ($OFI_t = e_{b,t} - e_{a,t}$), multi-level depth weighting, price impact regression ($\Delta P_t = \beta \cdot OFI_t$), market depth resilience ($D = 1/\beta$), and queue liquidity lab
- Jim Gatheral (2010) Transient Market Impact & Resiliency, decaying kernel ($G(\tau) = \lambda e^{-\rho\tau} + \gamma_{\text{perm}}$), Fredholm integral optimal liquidation, post-trade price relaxation, and No-Dynamic-Arbitrage price manipulation theorem lab
- Richard Roll (1984) Effective Spread & Serial Covariance, bid-ask bounce autocovariance ($S = 2\sqrt{-\text{Cov}(\Delta P_t, \Delta P_{t-1})}$), positive covariance puzzle, microstructure noise ratio, and return variance decomposition lab
- Corwin & Schultz (2012) High-Low Spread Estimator, daily extreme prices ($H_t, L_t$), single-day vs two-day variance scaling ($\beta = [\ln(H/L)]^2, \gamma = [\ln(H_{12}/L_{12})]^2$), closed-form spread ($S = \frac{2(e^\alpha - 1)}{1 + e^\alpha}$), Parkinson (1980) volatility de-biasing, and negative spread truncation lab
- Glosten-Milgrom (1985) Sequential Trade Microstructure, Bayesian quote updating ($A_t = \mathbb{E}[V \mid \text{Buy}], B_t = \mathbb{E}[V \mid \text{Sell}]$), adverse selection spread ($S_t = A_t - B_t$), martingale belief convergence ($p_t \to \mathbf{1}_{\{V=V_H\}}$), and spread collapse lab
- Easley-Kiefer-O'Hara-Paperman (1996) Probability of Informed Trading (PIN), daily information event tree ($\alpha, \delta$), Poisson arrival mixture ($\mu, \epsilon$), joint log-likelihood surface optimization, adverse selection risk, and PIN ($\frac{\alpha\mu}{\alpha\mu+2\epsilon}$) lab
- Hasbrouck (1991) Vector Autoregression (VAR) & Impulse Response, midquote revisions ($r_t$), signed order flow ($x_t$), contemporaneous quote impact ($b_0$), permanent informational price impact ($I(\infty) = \sum \beta_s$), transitory inventory friction, and Beveridge-Nelson quote variance decomposition ($R_w^2$) lab
- Kyle & Obizhaeva (2016) Market Microstructure Invariance, risk transfer business time ($W = V\sigma/C$), universal power laws (bet size $Q^* \propto (V/\sigma)^{1/3}$, spread $S \propto (\sigma^2/V)^{1/3}$, impact $I^*$), cross-asset invariance collapse, and square-root metaorder slippage lab
- Engle & Russell (1998) Autoregressive Conditional Duration (ACD), high-frequency point processes, trade timing ($\psi_i = \omega + \alpha x_{i-1} + \beta \psi_{i-1}$), Weibull baseline hazard dynamics ($h(t)$), duration clustering, and trade intensity volatility acceleration lab
- Ho & Stoll (1981) Optimal Dealer Pricing & Inventory Risk, CARA expected utility, reservation price skewing ($R(S,q) = S - q\gamma\sigma^2(T-t)$), asymmetric bid-ask half-spreads ($\delta_a^*, \delta_b^*$), and inventory mean-reversion lab
- Hawkes (1971) Self-Exciting Point Process, Ogata (1981) thinning algorithm, branching ratio ($\eta = \alpha/\beta$), endogenous order reflexivity, memory half-life ($t_{1/2} = \frac{\ln 2}{\beta}$), cubic variance scaling ($1/(1-\eta)^3$), and flash crash liquidity cascades lab
- Bouchaud, Gefen, Potters, & Wyart (2004) Propagator Model of Market Impact, long-memory order flow ($C(l) \sim l^{-\gamma}$), bare power-law propagator kernel ($G(l) = \frac{\Gamma_0}{(1+l)^\beta}$), critical balance efficiency condition ($\beta = \frac{1-\gamma}{2}$), apparent permanent impact ($R_\infty$), and anomalous diffusion lab
- Cartea & Jaimungal (2014) Optimal Market Making with Alpha Signals & Drift, Ornstein-Uhlenbeck signal dynamics ($d\alpha_t = -\kappa\alpha_t dt + \sigma_\alpha dW_t^\alpha$), HJB stochastic control, directional quote leaning ($\delta_a^* - \delta_b^*$), adverse selection mitigation, and inventory variance control lab
- Gatheral, Jaisson, & Rosenbaum (2018) Rough Volatility, Rough Bergomi (rBergomi) model, Riemann-Liouville fractional Brownian motion ($W_t^H$), sub-diffusive Hurst parameter ($H \approx 0.10 < 0.5$), monofractal structure function scaling ($\mathbb{E}[|\Delta \ln \sigma|^q] \propto \Delta^{qH}$), and short-dated ATM implied volatility skew power-law explosion ($\psi(\tau) \propto \tau^{H - 1/2}$) lab
- Guéant, Tapia, & Manziadi (2012) Dealing with Inventory Risk, closed-form market making, Cole-Hopf HJB linearization, tridiagonal matrix exponential ($v(\tau) = \exp(M\tau)\mathbf{1}$), exact inventory bounds ($q \in [-Q, +Q]$), and non-linear optimal bid-ask quote spreads ($\delta_b^*(q), \delta_a^*(q)$) lab
- Cont, Stoikov, & Talreja (2010) Stochastic Order Book Dynamics, continuous-time Markovian queues, birth-death intensity ($\lambda, \mu, \theta q$), 2D harmonic absorption probability ($p_1(x, y)$), expected queue depletion time ($E[\tau \mid q_0]$), and order book imbalance (OBI) lab
- Jim Gatheral (2004) & Gatheral-Jacquier (2014) Stochastic Volatility Inspired (SVI) Volatility Surface & Arbitrage, Raw SVI total variance ($w(k) = a + b[\rho(k-m) + \sqrt{(k-m)^2+\sigma^2}]$), Roger Lee asymptotic extreme-strike moment bounds ($b(1+|\rho|) \le 2$), Breeden-Litzenberger risk-neutral density, Durrleman butterfly no-arbitrage condition ($g(k) \ge 0$), and Jump-Wings (SVI-JW) conversion lab
- Rama Cont & Adrien de Larrard (2013) Price Dynamics in a Markovian Limit Order Book, heavy-traffic diffusion limit, conformal harmonic exit probability ($p_{\text{up}} = \frac{2}{\pi}\arctan(q_b / q_a)$), analytical microstructure volatility theorem ($\sigma = \frac{\delta}{D}\sqrt{\frac{\pi\mu}{4}}$), and $t^{-1/2}$ heavy-tailed price duration tails lab
- Peter Carr & Dilip Madan (1999) Option Valuation Using the Fast Fourier Transform (FFT), characteristic function inversion ($\phi_T(u)$), modified call damping factor ($\alpha > 0$), Simpson's quadrature weights ($w_j$), Nyquist reciprocal strike grid spacing ($\lambda \eta = \frac{2\pi}{N}$), and multi-strike implied volatility smile reconstruction lab
- Fang & Oosterlee (2008) Fourier-Cosine (COS) Series Expansion Option Pricing, characteristic function density projection ($A_k = \frac{2}{b-a}\operatorname{Re}[\phi(\frac{k\pi}{b-a})e^{-ik\pi\frac{a}{b-a}}]$), cumulant-based truncation bounds ($[c_1 - L\sqrt{c_2 + \sqrt{c_4}}, c_1 + L\sqrt{c_2 + \sqrt{c_4}}]$), closed-form payoff coefficients ($\chi_k, \psi_k$), analytical Greeks ($\Delta, \Gamma$), and exponential spectral convergence lab
- Longstaff & Schwartz (2001) Least Squares Monte Carlo (LSM) American Option Pricing, cross-sectional OLS regression on in-the-money paths, dynamic programming backward induction, optimal stopping times ($\tau^*$), dynamic early exercise boundary extraction ($S^*(t)$), and Early Exercise Premium (EEP) decomposition lab
- Brace, Gatarek, & Musiela (1997) LIBOR Market Model (BGM / LMM), discrete forward rate SDE dynamics ($dL_k/L_k = \mu_k dt + \sigma_k dW_t$), Spot LIBOR numeraire measure drift adjustments, Rebonato humped parametric volatility ($\sigma(t, T_k)$), Hunter-Jäckel-Joshi predictor-corrector stepping, Black-76 caplet benchmark calibration, and Rebonato swaption volatility approximation lab
- Hayne Leland (1994) & Leland-Toft (1996) Corporate Debt, Endogenous Default Barrier ($V_B^* = \frac{(1-\tau_c)C}{r}\frac{X}{1+X}$), smooth-pasting condition ($\partial E/\partial V = 0$), debt tax shields ($\text{TB}(V)$), bankruptcy costs ($\text{BC}(V)$), trade-off theory optimal capital structure ($C^*$), and credit spread term structure lab
- Darrell Duffie & Kenneth J. Singleton (1999) Reduced-Form Credit Risk, defaultable bond valuation, Recovery of Market Value (RMV), default-adjusted short rate ($R_t = r_t + \lambda_t L_t$), affine CIR hazard rate intensity ($\lambda_t$), credit spread term structures, and CS01 lab
- Robert Jarrow, David Lando, & Stuart Turnbull (JLT 1997) Credit Rating Migration, Markov chain transition matrices ($P, Q = \Pi P$), absorbing default state, multi-period matrix powers ($P^t$), credit spread term structures across rating classes, forward migration revaluation, and CreditMetrics CreditVaR lab
- Oldrich Vasicek (1987, 2002) Asymptotic Single Risk Factor (ASRF) Credit Portfolio Model, Gaussian latent factor returns ($X_i = \sqrt{\rho}Y + \sqrt{1-\rho}Z_i$), loss distribution CDF ($F(x)$), 99.9% Value at Risk ($\text{VaR}_{0.999}$), Expected Shortfall (CVaR), Basel II/III IRB regulatory capital requirement ($K$), RWA, maturity adjustments ($\text{MA}$), and Gordy (2003) granularity adjustments lab
- David X. Li (2000) Gaussian Copula & Synthetic CDO Tranche Pricing, one-factor latent asset returns ($X_i = \sqrt{\rho}M + \sqrt{1-\rho}Z_i$), Large Homogeneous Portfolio (LHP) conditional default probabilities ($p(t|m)$), protection and premium legs, equity upfront fees, mezzanine/senior breakeven par spreads, compound correlation smiles, and Base Correlation mapping lab
- CreditMetrics (1997, J.P. Morgan) Multi-Obligor Portfolio CreditVaR, S&P 8-state rating transition thresholds ($Z_{i, s} = \Phi^{-1}(\sum P_{i, m})$), correlated Gaussian latent asset returns via Cholesky decomposition ($\mathbf{Z} = \mathbf{L}\boldsymbol{\epsilon}$), forward credit yield curve revaluation, default recovery valuation, analytical portfolio credit volatility ($\sigma_{\text{port}}$), 99% CreditVaR, Expected Shortfall (CVaR), and marginal component risk contribution decomposition lab
- CreditRisk+ (1997, CSFP) Actuarial Credit Portfolio Risk, integer unit exposure bands ($\nu_i = \text{round}(E_i/L_0)$), Poisson point processes, Gamma-distributed systematic factor clustering ($S \sim \text{Gamma}(\alpha, \beta)$), Negative Binomial default counts, probability generating functions ($G_L(z)$), Panjer recursion / FFT inversion, exact analytical portfolio loss distributions, 99% CreditVaR, Expected Shortfall (CVaR), and sector risk contributions lab
- KMV (1993, Moody's Analytics) Structural Credit Risk & PortfolioManager, Black-Scholes-Merton asset inversion ($V_A, \sigma_A$), empirical default point ($D = \text{STD} + 0.5\text{LTD}$), Distance to Default ($DD$), empirical Expected Default Frequency (EDF™) mapping vs Normal $\Phi(-DD)$ fat-tail divergence, multi-obligor correlated asset return Monte Carlo simulation, CreditVaR, and Component Unexpected Loss (CUL) lab
- CreditPortfolioView (1997, McKinsey / Thomas C. Wilson) Macroeconomic Credit Risk & Multi-Period Stress Testing, multi-factor econometric logit index ($Y_{j, t} = \beta_{j, 0} + \sum \beta_{j, k} X_{k, t}$), conditional default probability ($P_{j, t} = \frac{1}{1 + \exp(-Y_{j, t})}$), credit cycle index ($r_{j, t} = P_{j, t}/\bar{P}_j$), macroeconomic-conditioned rating migration matrices ($M_t = [P_{ik}(t)]$), CCAR/DFAST stress scenario simulation, and multi-obligor CreditVaR lab
- Heath-Jarrow-Morton (HJM 1992) Forward Rate Framework & Term Structure Dynamics, instantaneous forward rate SDEs ($df(t, T) = \alpha(t, T) dt + \sum \sigma_i(t, T) dW_i(t)$), no-arbitrage drift condition ($\alpha(t, T) = \sum \sigma_i(t, T) \int_t^T \sigma_i(t, u) du$), multi-factor volatility decomposition, money market numeraire accumulation ($B(t)$), zero-coupon bond martingale tests ($\mathbb{E}^{\mathbb{Q}}[P(t, T)/B(t)] = P(0, T)$), and European bond option / swaption valuation lab
- Black-Karasinski (BK 1991) Lognormal Short-Rate Model & Trinomial Lattice, lognormal diffusion ($d \ln r = [\theta(t) - a \ln r]dt + \sigma dW$), non-negative interest rate guarantee ($r(t) > 0$), recombining trinomial tree construction, Arrow-Debreu state price forward induction calibration ($\sum Q_{i, j} e^{-r_{i, j} \Delta t} = P(0, t_{i+1})$), callable and puttable corporate bond pricing, embedded option decomposition, and negative convexity lab
- Two-Factor Hull-White (G2++) Gaussian Model, additive two-factor short rate ($r(t) = x(t) + y(t) + \varphi(t)$), exact term structure calibration ($\varphi(t)$), analytical zero-coupon bond pricing ($P(t, T, x, y)$), forward rate de-correlation ($\text{Corr}(df(t, T_1), df(t, T_2)) < 1$), yield curve twist/slope dynamics, and European swaption valuation via Brigo-Mercurio 1D numerical quadrature lab
- CIR++ (Extended Cox-Ingersoll-Ross) Model, square-root diffusion ($dx = k(\theta - x)dt + \sigma \sqrt{x}dW$), exact market yield curve calibration via deterministic shift ($\varphi(t) = f^M(0, t) - f^{\text{CIR}}(0, t)$), Feller non-negativity condition ($2k\theta \ge \sigma^2$), analytical European bond options via non-central chi-square CDFs, and closed-form European swaption valuation via Jamshidian decomposition lab
- Cheyette (1992) Markovian HJM Model, separable exponential volatility reduction ($\sigma(t, T) = \sigma(t)e^{-\kappa(T-t)}$), 2D Markovian state space ($dx = (y - \kappa x)dt + \sigma dW, dy = (\sigma^2 - 2\kappa y)dt$), exact zero-coupon bond pricing ($P(t, T)$), forward curve convexity adjustment, Jamshidian (1989) closed-form European swaption decomposition, and Monte Carlo martingale validation lab
- Multi-Curve Interest Rate Framework & Tenor Basis Swaps, post-2008 CSA collateralized discounting ($P^D(0, T)$ via OIS/SOFR/€STR), distinct forward rate projection curves ($F_{3M}, F_{6M}$), dual-curve bootstrapping, closed-form breakeven tenor basis spreads ($s_{3M/6M}$), and single-curve pricing divergence lab
- Cross-Currency Basis Swap (XCS) & CIP Parity Breakdown, Vladimir Piterbarg (2006, 2010) foreign collateral discounting theorem ($P_f^{\$}(0, T) = (S_0 / F(0, T)) P_{\$}(0, T)$), structural USD funding premia, closed-form breakeven basis spread ($s_{\text{XCS}}$), and Mark-to-Market (MtM Resettable) vs Constant Notional swap risk lab
- Mortgage-Backed Securities (MBS) Prepayment Modeling & Negative Convexity, Richard & Roll (1989) structural 4-factor prepayment model (Refinancing S-Curve, Seasoning, Seasonality, Burnout), PSA benchmark curves, SMM/CPR conversions, downward concavity, effective duration, and Option-Adjusted Spread (OAS) decomposition lab
- Collateralized Mortgage Obligation (CMO) Tranche Waterfall & Structuring, sequential pay tranches (A, B, C), Planned Amortization Class (PAC) collar bands ($\min(\text{PSA}_{\text{lower}}, \text{PSA}_{\text{upper}})$), companion/support tranche volatility absorption, Z-tranche accrual interest capitalization, and Stripped MBS (IO vs PO) negative duration divergence lab
- Collateralized Loan Obligation (CLO) Tranche Waterfall & Coverage Tests, leveraged loan collateral dynamics, 6-tranche capital structure (AAA to Equity), Overcollateralization (OC) and Interest Coverage (IC) compliance tests, automatic cash diversion / deleveraging triggers, Reinvestment vs Amortization period management, and equity excess spread IRR lab
- Credit Card Asset-Backed Securities (ABS) Master Trust & Excess Spread, revolving master trust cash flows, gross portfolio yield (APR + interchange), monthly excess spread waterfall ($\text{Yield} - (\text{Coupon} + \text{Servicing} + \text{Charge-offs})$), 3-month rolling average covenant, automatic Early Amortization (Payout Event) tripwires ($\le 0.00\%$), Monthly Payment Rate (MPR) principal paydown velocity, Seller's Interest dilution buffering, and Class A/B/C deleveraging lab
- Commercial Mortgage-Backed Securities (CMBS) Conduit & Defeasance, multi-property CRE collateral pools, Debt Yield ($\text{NOI} / \text{Loan}$) vs DSCR underwriting, Defeasance vs Yield Maintenance prepayment friction, Appraisal Reduction Amounts ($\text{ARA}$) and interest shortfall penetration, balloon refinancing shocks, and sequential tranche deleveraging lab
- Auto Loan Asset-Backed Securities (ABS) & Cumulative Net Loss (CNL), retail auto installment contract pools, Absolute Prepayment Speed ($\text{ABS} = \text{SMM} / [1 + \text{SMM}(m-1)]$), empirical loss timing curves (depreciation hump at M12-M24), vehicle repossession and wholesale auction recovery, Overcollateralization target and Turbo Amortization paydown, Reserve Account replenishment, and rating agency loss coverage multiples lab
- Equipment Lease Asset-Backed Securities (ABS) & Residual Value Risk, commercial equipment lease pools, Fair Market Value (FMV) vs $1 Buyout Capital leases, Discounted Residual Value (DRV) formula, rating agency stress haircuts ($H_{\text{residual}} \in [20\%, 50\%]$), turn-back adverse selection, remarketing lag, reserve fund liquidity, and Turbo Amortization cash trapping lab
- Whole Business Securitization (WBS) & Franchise Royalty Waterfalls, brand IP ring-fencing, master issuer SPV structure, system-wide sales and royalty collections, Cash Flow Available for Debt Service (CFADS), multi-tier DSCR covenants (1.75x 50% Cash Trap, 1.50x 100% Cash Trap, 1.20x Rapid Amortization sweep, 1.10x Manager Termination Default), and Anticipated Repayment Date (ARD) step-up penalty interest lab
- Student Loan Asset-Backed Securities (SLABS) & Parity Waterfall, Federal FFELP (97% statutory guarantee) vs Private credit pools, Special Allowance Payments (SAP) yield subsidies, borrower status migration (In-School / Grace, Deferment / Forbearance, Active Repayment), capitalized interest accumulation ($B_t \leftarrow B_{t-1} + \text{CapInt}$), bell-shaped Cohort Default Rate (CDR) timing curves, Asset-to-Debt Parity Ratios (Total Parity vs Senior Parity), and contractual Turbo Amortization cash sweeps (triggered below 105.0% target) lab
- Barrier option pricing (Up/Down & In/Out), barrier pin risk, discontinuous Greeks, hitting probability, and in-out parity lab
- Black-76 (1976) options on futures, commodity options, interest rate caplets, swaption valuation, and forward Greeks lab
- Bjerksund-Stensland (1993) American option pricing, closed-form flat boundary approximation, early exercise premiums, and Greeks lab
- Barone-Adesi & Whaley (1987) American option pricing, critical early-exercise boundary, quadratic approximation, and early exercise premium lab
- Garman-Kohlhagen (1983) FX option pricing, covered interest parity, dual interest rate Greeks, and forward delta surfaces lab
- Merton (1976) jump-diffusion option pricing, compound Poisson jumps, lognormal jump sizes, and volatility smile lab
- SABR stochastic volatility model, Hagan asymptotic Black implied volatility smile formula, backbone dynamics, and CEV elasticity lab
- Heston (1993) stochastic volatility model, Fourier inversion pricing, Black-Scholes implied volatility smile/skew, and CIR variance dynamics lab
- Black-Derman-Toy (BDT 1990) lognormal short-rate binomial lattice, term structure calibration, callable bond pricing, and negative convexity lab
- Hull-White (1990) one-factor short-rate model, exact initial term structure calibration, zero-coupon bond options, caplet pricing, and trinomial tree lab
- Cox-Ingersoll-Ross model (CIR 1985), square-root diffusion, Feller condition non-negativity, analytical zero-coupon pricing, and term structure lab
- Vasicek short-rate model (1977), Ornstein-Uhlenbeck stochastic diffusion, analytical zero bond pricing, term structure of yields, and convexity drag lab
- Ohlson Clean Surplus Model (1995), Linear Information Dynamics (LID), abnormal earnings persistence, other information, and book value convergence lab
- Bond Portfolio Immunization, classical Redington conditions, duration matching, convexity surplus, and Fong-Vasicek M² dispersion lab
- Walter's Model of dividend policy, optimal payout optimization, internal return vs. cost of capital, and reinvestment value lab
- Cox-Ross-Rubinstein binomial option pricing, recombining lattice, backward induction, American early exercise premium, and delta hedge lab
- Treynor-Black model, active security analysis, appraisal ratio weighting, beta-adjusted active allocation, and Sharpe expansion lab
- Modified Jones Model, total accruals, non-discretionary decomposition, revenue manipulation detection, and discretionary accruals lab
- Black-Litterman portfolio optimization, reverse optimization equilibrium returns, Bayesian view updating, and active tilt lab
- Debt capacity, maximum leverage sizing, multi-covenant bottlenecks, and borrowing headroom lab
- Fama-French 3-factor and 5-factor model, SMB size, HML value, RMW profitability, CMA investment, and multi-factor alpha lab
- Merton structural credit model (1974), Distance to Default (DD), Expected Default Frequency (EDF), and implied credit spread lab
- Ohlson O-Score, 9-factor logit econometric bankruptcy model, 2-year default probability, leverage pressure, and credit distress lab
- Zmijewski X-Score, probit econometric distress model, default probability %, financial leverage, and liquidity distress lab
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