# Neural network regression for Bermudan option pricing

## TL;DR

This paper explores neural network methods for approximating conditional expectations in Bermudan option pricing, demonstrating convergence and numerical efficiency as an alternative to traditional regression techniques.

## Contribution

It proves the convergence of the Longstaff and Schwartz algorithm when replacing regression with neural networks and shows their practical efficiency.

## Key findings

- Neural networks can effectively approximate conditional expectations in high-dimensional settings.
- The neural network approach converges under the same conditions as classical regression methods.
- Numerical experiments confirm the efficiency of neural networks over traditional regression in option pricing.

## Abstract

The pricing of Bermudan options amounts to solving a dynamic programming principle, in which the main difficulty, especially in high dimension, comes from the conditional expectation involved in the computation of the continuation value. These conditional expectations are classically computed by regression techniques on a finite dimensional vector space. In this work, we study neural networks approximations of conditional expectations. We prove the convergence of the well-known Longstaff and Schwartz algorithm when the standard least-square regression is replaced by a neural network approximation. We illustrate the numerical efficiency of neural networks as an alternative to standard regression methods for approximating conditional expectations on several numerical examples.