用深度模型学习波动率与情绪,提升中证300期权定价精度。
Deep g-Pricing for CSI 300 Index Options with Volatility Trajectories and Market Sentiment
- 构建双网络框架,从数据中学习非线性定价机制。
- 相较BSM模型,平均绝对误差降低32.2%,百分比误差降35.3%。
- 情绪因子对看涨期权影响更大,波动率轨迹对看跌更均衡。
真实市场中的期权定价面临根本挑战。布莱克-斯科尔斯-默顿(BSM)模型假设波动率恒定,使用线性生成器 $g(t,x,y,z)=-ry$,且未显式引入行为因素,导致与实际动态系统性偏离。本文在深度前向-后向随机微分方程(FBSDE)框架下,通过学习非线性生成器扩展了BSM模型。提出双网络架构:价值网络 $u_θ$ 学习期权价格,生成器网络 $g_ϕ$ 揭示定价机制,对冲策略 $Z_t=σ_t X_t \nabla_x u_θ$ 由自动微分获得。该框架采用可学习初始值 $Y_0=u_θ(0,\cdot)$ 的前向递推,自然融合波动率轨迹与市场情绪特征。在中证300指数期权上的实证结果表明,相比BSM,本方法使平均绝对误差(MAE)降低32.2%,平均绝对百分比误差(MAPE)降低35.3%。可解释性分析显示,架构改进对所有期权类型均有效,但信息优势在认购与认沽间不对称:认购期权改善主要由情绪特征驱动,而认沽期权则受波动率轨迹与情绪特征共同影响,符合经济直觉。
原文摘要 · Abstract (English)
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.
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