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

arXiv: https://arxiv.org/abs/2601.18804 · HTML: https://mlsanity.com/paper/2601.18804/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 15 Jan 2026.

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [Learning Activation Functions to Improve Deep Neural Networks](https://mlsanity.com/paper/1412.6830/) (2014)

## Abstract (arXiv)

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 uθ learns option prices and the generator network gφ characterizes the pricing mechanism, with the hedging strategy Zt=σt Xt nablax uθ obtained via automatic differentiation. The framework adopts forward recursion from a learnable initial condition Y0=uθ(0,·), 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.