# Simultaneous upper and lower bounds of American-style option prices with hedging via neural networks

## TL;DR

This paper presents two neural network-based methods to efficiently compute both upper and lower bounds of American-style option prices and derive hedging strategies, avoiding nested simulations and enabling high-dimensional pricing.

## Contribution

Introduces two novel neural network approaches for simultaneous upper and lower bound estimation of American options without nested Monte Carlo.

## Key findings

- Reduces computational complexity for high-dimensional options
- Provides effective hedging strategies and variance reduction techniques
- Demonstrates accurate bounds through numerical experiments

## Abstract

In this paper, we introduce two novel methods to solve the American-style option pricing problem and its dual form at the same time using neural networks. Without applying nested Monte Carlo, the first method uses a series of neural networks to simultaneously compute both the lower and upper bounds of the option price, and the second one accomplishes the same goal with one global network. The avoidance of extra simulations and the use of neural networks significantly reduce the computational complexity and allow us to price Bermudan options with frequent exercise opportunities in high dimensions, as illustrated by the provided numerical experiments. As a by-product, these methods also derive a hedging strategy for the option, which can also be used as a control variate for variance reduction.