Deep g-Pricing for CSI 300 Index Options with Volatility Trajectories and Market Sentiment

TL;DR

This paper introduces a deep learning-based extension to the Black-Scholes-Merton model that incorporates volatility trajectories and market sentiment, significantly improving pricing accuracy for CSI 300 index options.

Contribution

It develops a novel dual-network deep FBSDE framework that learns a nonlinear generator and integrates behavioral factors into option pricing.

Findings

Reduces MAE by 32.2% compared to BSM

Reduces MAPE by 35.3% compared to BSM

Sentiment features mainly improve call option pricing

Abstract

Option pricing in real markets faces fundamental challenges. The Black--Scholes--Merton (BSM) model assumes constant volatility and uses a linear generator $g(t,x,y,z)=-ry$, while lacking explicit behavioral factors, resulting in systematic departures from observed dynamics. This paper extends the BSM model by learning a nonlinear generator within a deep Forward--Backward Stochastic Differential Equation (FBSDE) framework. We propose a dual-network architecture where the value network $u_\theta$ learns option prices and the generator network $g_\phi$ characterizes the pricing mechanism, with the hedging strategy $Z_t=\sigma_t X_t \nabla_x u_\theta$ obtained via automatic differentiation. The framework adopts forward recursion from a learnable initial condition $Y_0=u_\theta(0,\cdot)$, naturally accommodating volatility trajectory and sentiment features. Empirical results on CSI 300 index options show that our method reduces Mean Absolute Error (MAE) by 32.2\% and Mean Absolute Percentage Error (MAPE) by 35.3\% compared with BSM. Interpretability analysis indicates that architectural improvements are effective across all option types, while the information advantage is asymmetric between calls and puts. Specifically, call option improvements are primarily driven by sentiment features, whereas put options show more balanced contributions from volatility trajectory and sentiment features. This finding aligns with economic intuition regarding option pricing mechanisms.