The Pricing of American Options on the Quantum Computer

22 Pages Posted: 7 Feb 2023 Last revised: 5 May 2023

Date Written: February 7, 2023


An American option valuation and finding the optimal stopping time are among the most critical problems in option pricing theory and derivatives valuation. The classical approaches use the dynamic programming principle, so parallelizing is hard. Because we need to store the continuation values for all paths to do one dynamic programming step, we are limited in the number of simulations that can be processed by the memory size available on the classical computer.

This paper proposes a novel approach to pricing American options on quantum computers. Before the article, only one method for that purpose was proposed. The novel algorithm combines Quantum Binomial Tree and Quantum Machine Learning to implement the direct method for pricing American options on a quantum computer. It utilizes the quantum amplitude estimation algorithm with a quadratic speed-up over the classical Monte Carlo. This method allows us to exploit the exponential growth in the state vector on quantum computers and, by this, to overcome the limitations on memory on classical techniques.

Keywords: Quantum Monte Carlo, Pricing derivatives, Quantum Computing, Quantum Machine Learning

Suggested Citation

Pracht, Rafał, The Pricing of American Options on the Quantum Computer (February 7, 2023). Available at SSRN: or

Rafał Pracht (Contact Author)

BNP Paribas Bank Polska ( email )


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