# Data-driven Hedging of Stock Index Options via Deep Learning

arXiv: https://arxiv.org/abs/2111.03477 · HTML: https://mlsanity.com/paper/2111.03477/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 5 Nov 2021.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations](https://mlsanity.com/paper/1706.04702/) (2017)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Deep Learning Approximation for Stochastic Control Problems](https://mlsanity.com/paper/1611.07422/) (2016)
- [Deep Learning for Ranking Response Surfaces with Applications to Optimal Stopping Problems](https://mlsanity.com/paper/1901.03478/) (2019)

## Built on by (most cited first, 1 of 1)

- [Enhancing Black-Scholes Delta Hedging via Deep Learning](https://mlsanity.com/paper/2407.19367/) (2024)

## Abstract (arXiv)

We develop deep learning models to learn the hedge ratio for S&P500 index options directly from options data. We compare different combinations of features and show that a feedforward neural network model with time to maturity, Black-Scholes delta and a sentiment variable (VIX for calls and index return for puts) as input features performs the best in the out-of-sample test. This model significantly outperforms the standard hedging practice that uses the Black-Scholes delta and a recent data-driven model. Our results demonstrate the importance of market sentiment for hedging efficiency, a factor previously ignored in developing hedging strategies.