Quantum algorithm for stochastic optimal stopping problems with applications in finance

TL;DR

This paper introduces a quantum algorithm for stochastic optimal stopping problems, leveraging quantum computing to achieve nearly quadratic speedup over classical methods, with applications in financial option pricing.

Contribution

It presents a novel quantum version of the least squares Monte Carlo algorithm, integrating quantum access, quantum circuits, and quantum Monte Carlo techniques for improved efficiency.

Findings

Achieves nearly quadratic speedup over classical LSM algorithm.

Applicable to American option pricing with Brownian motion models.

Analyzes case studies demonstrating quantum algorithm advantages.

Abstract

The famous least squares Monte Carlo (LSM) algorithm combines linear least square regression with Monte Carlo simulation to approximately solve problems in stochastic optimal stopping theory. In this work, we propose a quantum LSM based on quantum access to a stochastic process, on quantum circuits for computing the optimal stopping times, and on quantum techniques for Monte Carlo. For this algorithm, we elucidate the intricate interplay of function approximation and quantum algorithms for Monte Carlo. Our algorithm achieves a nearly quadratic speedup in the runtime compared to the LSM algorithm under some mild assumptions. Specifically, our quantum algorithm can be applied to American option pricing and we analyze a case study for the common situation of Brownian motion and geometric Brownian motion processes.