Paper: arXiv 2601.18804

Authors: Yilun Zhang, Zheng Tang, Hexiang Sun, Yufeng Shi

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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 8.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a novel deep learning framework for option pricing by embedding learned nonlinear generators into a forward-backward stochastic differential equation (FBSDE). It features a rigorous empirical validation on CSI 300 index options, integrating predicted realized volatility trajectories and sentiment features extracted via Large Language Models while offering thorough interpretability analysis.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Improve CSI 300 Option Pricing via Nonlinear FBSDE"] --> B["Data Inputs:<br>Asset Prices, Volatility Trajectories & Market Sentiment"]
    B --> C["Dual-Network Architecture:<br>Value Net u_θ & Generator Net g_φ"]
    C --> D["FBSDE Forward Recursion:<br>Learn Pricing Mechanism & Derive Hedging via Auto-Diff"]
    D --> E["Empirical Evaluation:<br>Performance Benchmarking vs. BSM Model"]
    E --> F["Key Findings:<br>MAE -32.2%, MAPE -35.3%<br>Asymmetric Drivers: Calls (Sentiment), Puts (Vol + Sentiment)"]

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1 of 63 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.