Undergraduate Honors Thesis Presentation: Dynamic Lambda Estimation in High-Frequency Market Making

This thesis develops a dynamic market-making strategy that improves upon existing models by adapting to time-varying liquidity conditions. Building on the discrete-time stochastic liquidity-demand framework of Capponi, Figueroa-López, and Yu (2021), which uses a Bellman equation approach to derive optimal bid and ask quotes under inventory constraints, we propose a novel extension that allows the liquidation-cost parameter lambda to evolve dynamically. Rather than fixing lambda across the trading horizon, we estimate it daily using least squares regression on simulated liquidation data, then apply ARIMA forecasting to predict future values. These dynamically updated lambda estimates are inserted into the Bellman-based control problem at each step, allowing the model to respond to evolving market depth and price impact. Empirical results on high-frequency limit order book data demonstrate that our dynamic-lambda strategy reduces end-of-day inventory and improves terminal wealth compared to fixed-lambda benchmarks, offering a more adaptive and resilient approach to high-frequency market making.

Advisor: José E. Figueroa-López