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

TL;DR

This work tackles the limitations of constant-volatility pricing by embedding volatility trajectories and market sentiment into a deep g-pricing framework based on a dual-network deep FBSDE. It jointly learns a value function and a contract-conditioned generator, computes hedging via automatic differentiation, and uses a forward recursion from a learnable initial value to fuse information adaptively. Empirical results on CSI 300 index options show substantial improvements over BSM and a prior deep BSDE model, with MAE reductions of $32.2\%$ and MAPE reductions of $35.3\%$, and detailed interpretability analyses revealing asymmetric information dependence between calls and puts. The approach delivers a transparent, economically meaningful pricing mechanism with practical implications for risk management and derivatives trading.

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 $u_θ$ learns option prices and the generator network $g_φ$ characterizes the pricing mechanism, with the hedging strategy $Z_t=σ_t X_t \nabla_x u_θ$ obtained via automatic differentiation. The framework adopts forward recursion from a learnable initial condition $Y_0=u_θ(0,\cdot)$, 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.

Figures (4)

• Figure 1: Architecture of the value network and generator network. The left panel shows the value network, illustrating the financial variable expansion layer, sentiment feature embedding layer with learnable gating parameter, shared backbone, and dual-head output architecture. The right panel shows the generator network, which has a similar architecture but additionally receives $Y_t$ and $Z_t$ as inputs.
• Figure 2: Loss Function Curves of Two-Stage Training
• Figure 3: Scatter Plots of Predicted versus Actual Values across Different Moneyness Levels
• Figure 4: Shapley Value Decomposition Results