Algorithmic Market Making Predictive Alpha Drift Signals Cartea & Jaimungal (2014)

Cartea-Jaimungal (2014) Market Making Lab

Simulate Álvaro Cartea and Sebastian Jaimungal's (2014) optimal market making framework. Model Ornstein-Uhlenbeck short-term alpha signals, asymmetric quote leaning, toxic flow defense, and multi-agent PnL benchmarking.

Theoretical Foundations: Stochastic Optimal Control with Predictive Drift & Inventory Risk
1. Price Process with Mean-Reverting Alpha Drift

The mid-price $S_t$ exhibits stochastic volatility and an instantaneous predictive drift signal $\alpha_t$ governed by an Ornstein-Uhlenbeck process:

$$dS_t = \alpha_t dt + \sigma dW_t^S, \quad d\alpha_t = -\kappa_\alpha \alpha_t dt + \sigma_\alpha dW_t^\alpha$$

The parameter $\kappa_\alpha$ governs the signal's mean-reversion speed with memory half-life $t_{1/2} = \frac{\ln 2}{\kappa_\alpha}$, reflecting ephemeral order flow imbalance (OFI) dynamics.

2. HJB Optimal Quoting Offsets & Directional Leaning

Solving the Hamilton-Jacobi-Bellman PDE with inventory penalty $\phi q^2$ yields the closed-form optimal half-spreads $\delta_a^*$ and $\delta_b^*$:

$$\delta_a^*(q, \alpha) = s_0 + \frac{2q - 1}{2}\zeta - \chi \alpha_t, \quad \delta_b^*(q, \alpha) = s_0 - \frac{2q + 1}{2}\zeta + \chi \alpha_t$$

When $\alpha_t > 0$ (bullish signal), quotes lean upward: $\delta_a^*$ widens to avoid adverse selection, while $\delta_b^*$ tightens to aggressively buy inventory ahead of the price jump.

Model Parameters

HFT Order Flow Imbalance (OFI) Desk: Fast mean-reverting alpha (κ = 4.0, half-life = 0.17s) typical of short-term order book imbalance signals.

Cartea-Jaimungal PnL +$14.82 Alpha + Inv
Alpha Advantage +$5.20 Alpha Outperformance
Avellaneda-Stoikov PnL +$9.62 Inventory Only
Naive Fixed Quoter -$2.45 Fixed Spread
Final CJ Inventory +2 shares
Inventory Variance 1.84
Total Executions 48 (25B / 23S)
Signal Half-Life $t_{1/2}$ 0.17 s
Dual 5×5 Microstructure Sensitivity Grids
Sensitivity Grid 1: Inventory $q$ vs Alpha Drift $\alpha$ → Quote Skew $(\delta_a^* - \delta_b^*)$

Demonstrates how predictive alpha drift offsets inventory shading to lean quotes competitively:

Sensitivity Grid 2: Signal Decay $\kappa_\alpha$ vs Signal Vol $\sigma_\alpha$ → Alpha Edge (bps)

Quantifies expected alpha information value across signal persistence and volatility:

Market Microstructure Mastery: Cartea-Jaimungal Optimal Quoting
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Frequently Asked Questions: Cartea-Jaimungal Model & Predictive Alpha Quoting

The Cartea and Jaimungal (2014) model is the modern benchmark for algorithmic high-frequency market making. It extends the classic Avellaneda-Stoikov framework by incorporating short-term predictive price drift (alpha signals) into the Hamilton-Jacobi-Bellman (HJB) stochastic optimal control problem, optimizing bid and ask quotes to harvest alpha while controlling inventory risk.

When the alpha signal is positive (bullish drift), the market maker shifts quotes upward by subtracting $\chi \alpha_t$ from the ask offset and adding $\chi \alpha_t$ to the bid offset. This widens the ask to prevent selling into rising prices, while tightening the bid to aggressively accumulate inventory before the anticipated price increase.

In the Cartea-Jaimungal framework, the alpha signal $\alpha_t$ is modeled as a mean-reverting Ornstein-Uhlenbeck process $d\alpha_t = -\kappa_\alpha \alpha_t dt + \sigma_\alpha dW_t^\alpha$. This captures the transient nature of high-frequency microstructural signals, such as order book imbalance (OFI), which decay rapidly as orders are executed.

Avellaneda-Stoikov (2008) assumes the mid-price is a driftless martingale and optimizes quoting purely to minimize inventory variance. Cartea-Jaimungal (2014) generalizes this by introducing non-zero predictable drift, demonstrating how market makers can actively lean their quotes to capture directional price trends while retaining inventory bounds.

Even with a strong alpha signal, trading without inventory penalties leads to runaway position sizes. If market conditions change or the predictive signal reverses, an unconstrained dealer faces catastrophic mark-to-market losses. The quadratic inventory penalty $\phi q^2$ ensures the dealer stays within manageable risk bounds.