# Neural Options Pricing

arXiv: https://arxiv.org/abs/2105.13320 · HTML: https://mlsanity.com/paper/2105.13320/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 21 references that are in the map.
- First posted on arXiv 27 May 2021.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Theoretical guarantees for sampling and inference in generative models with latent diffusions](https://mlsanity.com/paper/1903.01608/) (2019)
- [Infinitely deep neural networks as diffusion processes](https://mlsanity.com/paper/1905.11065/) (2019)
- [Deep Neural Network Framework Based on Backward Stochastic Differential Equations for Pricing and Hedging American Options in High Dimensions](https://mlsanity.com/paper/1909.11532/) (2019)
- [Pricing options and computing implied volatilities using neural networks](https://mlsanity.com/paper/1901.08943/) (2019)

## Abstract (arXiv)

This research investigates pricing financial options based on the traditional martingale theory of arbitrage pricing applied to neural SDEs. We treat neural SDEs as universal Ito process approximators. In this way we can lift all assumptions on the form of the underlying price process, and compute theoretical option prices numerically. We propose a variation of the SDE-GAN approach by implementing the Wasserstein distance metric as a loss function for training. Furthermore, it is conjectured that the error of the option price implied by the learnt model can be bounded by the very Wasserstein distance metric that was used to fit the empirical data.