Bermudan option pricing by quantum amplitude estimation and Chebyshev interpolation

Abstract

AbstractPricing 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 $\widetilde{O}(\epsilon ^{-1})$ O ˜ ( ϵ − 1 ) , where ϵ 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 $\widetilde{O}(\epsilon ^{-2})$ O ˜ ( ϵ − 2 ) .