Quantum-inspired variational algorithms for partial differential equations: Application to financial derivative pricing

TL;DR

This paper introduces a quantum-inspired variational algorithm that leverages neural networks and Monte Carlo methods to efficiently solve high-dimensional PDEs, demonstrated on complex financial derivative pricing models.

Contribution

It generalizes variational Monte Carlo techniques to arbitrary time-dependent PDEs, applying them to multi-asset Black-Scholes equations for option pricing.

Findings

Effective handling of high-dimensional PDEs

Accurate pricing of complex financial derivatives

Potential for quantum-inspired computational advantages

Abstract

Variational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of partial differential equations (PDEs); namely, the real- and imaginary time-dependent Schr\"odinger equation. In this paper, we present a simple generalization of VMC applicable to arbitrary time-dependent PDEs, showcasing the technique in the multi-asset Black-Scholes PDE for pricing European options contingent on many correlated underlying assets.