# Pricing options and computing implied volatilities using neural networks

arXiv: https://arxiv.org/abs/1901.08943 · HTML: https://mlsanity.com/paper/1901.08943/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jan 2019.

## Built on by (most cited first, 9 of 9)

- [Calibrated Physics-Informed Uncertainty Quantification](https://mlsanity.com/paper/2502.04406/) (2025)
- [Langevin dynamics based algorithm e-THvarepsilonO POULA for stochastic optimization problems with discontinuous stochastic gradient](https://mlsanity.com/paper/2210.13193/) (2022)
- [Data-driven initialization of deep learning solvers for Hamilton-Jacobi-Bellman PDEs](https://mlsanity.com/paper/2207.09299/) (2022)
- [Machine learning for option pricing: an empirical investigation of network architectures](https://mlsanity.com/paper/2307.07657/) (2023)
- [Neural Options Pricing](https://mlsanity.com/paper/2105.13320/) (2021)
- [Adaptive Nesterov Accelerated Distributional Deep Hedging for Efficient Volatility Risk Management](https://mlsanity.com/paper/2502.17777/) (2025)
- [Error Analysis of Deep PDE Solvers for Option Pricing](https://mlsanity.com/paper/2505.05121/) (2025)
- [Accuracy estimation of neural networks by extreme value theory](https://mlsanity.com/paper/2511.00490/) (2025)
- [Asymptotically-informed neural networks for Black-Scholes implied volatility computation](https://mlsanity.com/paper/2609.05491/) (2026)

## Abstract (arXiv)

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent's iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly.