Modeling Discrete-Time Option Pricing with Microstructure Noise A Gradient Boosting Framework for Binary Lattice Methods

Abstract

This paper proposes a generalized discrete-time option pricing framework that incorporates endogenous market microstructure noise through a gradient-boosting-optimized binary lattice model. Motivated by persistent volatility smirk anomalies in SPX options during the 2025 U.S. equity volatility compression episode and liquidity fragmentation in China’s CSI 300 index futures market, the study extends the classical binomial framework to account for high-frequency trading frictions, asymmetric information propagation, and order-flow-driven price discovery. The model constructs a microstructure-adapted risk-neutral measure and estimates transition probabilities using gradient boosting with a penalized objective function. Empirical analysis based on 46,655 minute-level observations of SPY shows that the proposed framework improves pricing accuracy and better captures volatility smirk dynamics than traditional lattice methods. In addition, generalized method of moments estimation confirms the statistical significance of the microstructure correction terms. The paper contributes a closed-form solution for microstructure-adjusted probabilities, a high-frequency GMM correction for time-scaling biases, and an integrated treatment of volatility smirk dynamics within a unified derivatives pricing framework. The results suggest that incorporating market microstructure effects can substantially enhance option valuation in modern high-frequency and fragmented markets.