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

TL;DR

This paper introduces a deep Recurrent Neural Network framework for efficiently pricing and hedging high-dimensional American options, offering improvements in computational time and memory over traditional methods.

Contribution

The paper presents a novel deep RNN approach that computes prices and deltas for American options across all time steps with linear time complexity and constant memory, outperforming feedforward networks.

Findings

The RNN framework provides accurate prices and deltas for American options.

It reduces computational time from quadratic to linear compared to feedforward networks.

It maintains constant memory usage, improving scalability.

Abstract

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.