# Efficient Pricing and Hedging of High Dimensional American Options Using Recurrent Networks

arXiv: https://arxiv.org/abs/2301.08232 · HTML: https://mlsanity.com/paper/2301.08232/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 36 references that are in the map.
- First posted on arXiv 19 Jan 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (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 Learning Approximation for Stochastic Control Problems](https://mlsanity.com/paper/1611.07422/) (2016)
- [Optimal Stopping via Randomized Neural Networks](https://mlsanity.com/paper/2104.13669/) (2021)
- [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)
- [Towards Robust and Stable Deep Learning Algorithms for Forward Backward Stochastic Differential Equations](https://mlsanity.com/paper/1910.11623/) (2019)

## Built on by (most cited first, 2 of 2)

- [Simultaneous upper and lower bounds of American-style option prices with hedging via neural networks](https://mlsanity.com/paper/2302.12439/) (2023)
- [Efficient Denoising using Score Embedding in Score-based Diffusion Models](https://mlsanity.com/paper/2404.06661/) (2024)

## Abstract (arXiv)

We propose a deep Recurrent neural network (RNN) framework for computing prices and deltas of American options in high dimensions. Our proposed framework uses two deep RNNs, where one network learns the price and the other learns the delta of the option for each timestep. Our proposed framework yields prices and deltas for the entire spacetime, not only at a given point (e.g. t = 0). The computational cost of the proposed approach is linear in time, which improves on the quadratic time seen for feedforward networks that price American options. The computational memory cost of our method is constant in memory, which is an improvement over the linear memory costs seen in feedforward networks. Our numerical simulations demonstrate these contributions, and show that the proposed deep RNN framework is computationally more efficient than traditional feedforward neural network frameworks in time and memory.