# Machine learning for option pricing: an empirical investigation of network architectures

arXiv: https://arxiv.org/abs/2307.07657 · HTML: https://mlsanity.com/paper/2307.07657/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 44 references that are in the map.
- First posted on arXiv 14 Jul 2023.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [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)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [Highway Networks](https://mlsanity.com/paper/1505.00387/) (2015)
- [Benefits of depth in neural networks](https://mlsanity.com/paper/1602.04485/) (2016)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Neural networks for option pricing and hedging: a literature review](https://mlsanity.com/paper/1911.05620/) (2019)
- [A generative adversarial network approach to calibration of local stochastic volatility models](https://mlsanity.com/paper/2005.02505/) (2020)
- [Deep neural networks algorithms for stochastic control problems on finite horizon: convergence analysis](https://mlsanity.com/paper/1812.04300/) (2018)
- [Solving high-dimensional optimal stopping problems using deep learning](https://mlsanity.com/paper/1908.01602/) (2019)
- [Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications](https://mlsanity.com/paper/1812.05916/) (2018)
- [Pricing options and computing implied volatilities using neural networks](https://mlsanity.com/paper/1901.08943/) (2019)
- [Computation of optimal transport and related hedging problems via penalization and neural networks](https://mlsanity.com/paper/1802.08539/) (2018)
- [Robust risk aggregation with neural networks](https://mlsanity.com/paper/1811.00304/) (2018)
- [Robust pricing and hedging of options on multiple assets and its numerics](https://mlsanity.com/paper/1909.03870/) (2019)
- [Randomized optimal stopping algorithms and their convergence analysis](https://mlsanity.com/paper/2002.00816/) (2020)
- [A deep learning approach to data-driven model-free pricing and to martingale optimal transport](https://mlsanity.com/paper/2103.11435/) (2021)

## Built on by (most cited first, 3 of 3)

- [Error Analysis of Deep PDE Solvers for Option Pricing](https://mlsanity.com/paper/2505.05121/) (2025)
- [Option Pricing on Noisy Intermediate-Scale Quantum Computers: A Quantum Neural Network Approach](https://mlsanity.com/paper/2604.19832/) (2026)
- [Asymptotically-informed neural networks for Black-Scholes implied volatility computation](https://mlsanity.com/paper/2609.05491/) (2026)

## Abstract (arXiv)

We consider the supervised learning problem of learning the price of an option or the implied volatility given appropriate input data (model parameters) and corresponding output data (option prices or implied volatilities). The majority of articles in this literature considers a (plain) feed forward neural network architecture in order to connect the neurons used for learning the function mapping inputs to outputs. In this article, motivated by methods in image classification and recent advances in machine learning methods for PDEs, we investigate empirically whether and how the choice of network architecture affects the accuracy and training time of a machine learning algorithm. We find that the generalized highway network architecture achieves the best performance, when considering the mean squared error and the training time as criteria, within the considered parameter budgets for the Black-Scholes and Heston option pricing problems. Considering the transformed implied volatility problem, a simplified DGM variant achieves the lowest error among the tested architectures. We also carry out a capacity-normalised comparison for completeness, where all architectures are evaluated with an equal number of parameters. Finally, for the implied volatility problem, we additionally include experiments using real market data.