Bermudan option pricing by quantum amplitude estimation and Chebyshev interpolation

TL;DR

This paper introduces a quantum algorithm for Bermudan option pricing that leverages Chebyshev interpolation and quantum amplitude estimation, achieving a quadratic speed-up over classical Monte Carlo methods.

Contribution

It presents a novel quantum approach combining Chebyshev interpolation with amplitude estimation for efficient Bermudan option pricing.

Findings

Achieves quadratic speed-up in oracle calls compared to classical methods.

Uses Chebyshev interpolation for continuation value approximation.

Scales as O(psilon^{-1}) in error tolerance.

Abstract

Pricing of financial derivatives, in particular early exercisable options such as Bermudan options, is an important but heavy numerical task in financial institutions, and its speed-up will provide a large business impact. Recently, applications of quantum computing to financial problems have been started to be investigated. In this paper, we first propose a quantum algorithm for Bermudan option pricing. This method performs the approximation of the continuation value, which is a crucial part of Bermudan option pricing, by Chebyshev interpolation, using the values at interpolation nodes estimated by quantum amplitude estimation. In this method, the number of calls to the oracle to generate underlying asset price paths scales as $\widetilde{O}(\epsilon^{-1})$, where $\epsilon$ is the error tolerance of the option price. This means the quadratic speed-up compared with classical Monte Carlo-based methods such as least-squares Monte Carlo, in which the oracle call number is $\widetilde{O}(\epsilon^{-2})$.