Synthetic Futures & Synthetic Stock Options Lab

Model institutional synthetic futures: Put-Call Parity forward replication, basis carry, delta linear tracking, capital efficiency, dividend risk, and Black-Scholes Greeks.

Strategy Presets:

Position Parameters

Replicates 100 shares of underlying equity per contract.
Forward Price (F_0)

$100.53

Cost of Carry S*e^((r-q)T)
Net Initial Cashflow

+$523

Call Prem minus Put Prem
Synthetic Net Delta

+1,000

Equiv to 1,000 Shares
Capital Efficiency

5.2x

Options vs Stock Margin
Expiration Payoff: Synthetic Future vs Outright Equity Breakeven Spot: $99.48
The synthetic position (blue line) perfectly overlaps outright stock (dashed gray line), offset only by the net financing carry.
Delta, Gamma, Vega, and Theta Components Linear Replication (Gamma = 0)
Call and put gammas and vegas cancel each other out identically, leaving a flat Δ = 1.0 curve with zero vega exposure.
Synthetic Forward Premium Across Calendar Days (DTE) Cost of Carry Curve
Displays how interest rate carry (r) and dividend yield (q) shape the forward price $F = S \cdot e^{(r-q)T}$ from 1 to 365 days.

Sensitivity: Spot Move (%) vs IV Shift Shock on Mark-to-Market P&L ($)

Sensitivity: Interest Rate (r) vs Dividend Yield (q) on Net Carry ($)

Institutional Mechanics of Synthetic Positions

1. Put-Call Parity Identity

Put-Call Parity dictates that holding a European call and shorting a European put at strike $K$ must equal buying the underlying stock financed by borrowing the present value of the strike: $$C(S, K, T) - P(S, K, T) = S_0 e^{-q T} - K e^{-r T}$$ At terminal expiration $T=0$, the payoff is strictly linear: $\max(0, S_T - K) - \max(0, K - S_T) = S_T - K$, reproducing outright long equity dollar-for-dollar.

2. Greek Cancellation & Convexity

Because Black-Scholes formulas for calls and puts share identical gamma $\Gamma_C = \Gamma_P$ and vega $\nu_C = \nu_P$, combining $+1$ Long Call with $-1$ Short Put results in exact cancellation: $$\Gamma_{\text{net}} = \Gamma_C - \Gamma_P = 0, \quad \nu_{\text{net}} = \nu_C - \nu_P = 0$$ The position has zero volatility sensitivity and behaves like a non-derivative asset with pure linear delta $\Delta_{\text{net}} = e^{-q T} \approx 1.0$.

3. Early Assignment & Pin Risk

Under American option conventions, the short leg carries early exercise liability. If holding a synthetic long and the stock falls deep in-the-money, the short put leg may be exercised early to capture interest carry. Conversely, for a synthetic short, an impending ex-dividend date can trigger early exercise on the short call, breaking the synthetic hedge and leaving an unhedged short stock borrow.

Synthetic Strategies Mastery Quiz

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Frequently Asked Questions

A Synthetic Long Future (or synthetic long stock) is an options strategy combining a long call option (+C) and a short put option (-P) at the exact same strike price (K) and expiration date (T). A Synthetic Short Future combines a short call (-C) and long put (+P). The combined position replicates the linear delta ($\Delta = 1.0$) and terminal payoff of holding outright equity shares or futures contracts.

Put-Call Parity states that $C - P = S e^{-q T} - K e^{-r T}$. At expiration ($T=0$), the net payoff $C - P$ is identically equal to $S_T - K$. Prior to expiration, the net premium difference reflects the discounted cost of carry: interest financing costs on strike $K$ minus dividends on underlying spot $S$.

Institutional traders utilize synthetic futures for substantial capital efficiency, lower initial margin requirements, seamless short exposure without hard-to-borrow locate fees, and synthetic basis arbitrage when option markets misprice the forward cost of carry.

A synthetic long position has a net Delta of approximately 1.0 (or $e^{-q T}$ for dividend-paying assets). Because long call gamma/vega exactly equals short put gamma/vega at the same strike, net Gamma is 0 and net Vega is 0. The position has zero curvature or volatility exposure, behaving like a purely linear asset.

The primary risks are uncapped linear directional exposure, margin call risk during adverse swings, and American-style early assignment hazard. For synthetic longs, the short put leg can be assigned early if it goes deep in the money; for synthetic shorts, the short call can be assigned prior to an ex-dividend date.