The Pricing of American options on the Quantum Computer

The valuation of American options and the determination of optimal stopping times remain central challenges in option pricing theory and derivatives valuation. Classical approaches to multidimensional problems rely on the dynamic programming principle, which is notoriously difficult to parallelize. Moreover, the need to store continuation values for all simulated paths in each dynamic programming step imposes severe memory constraints on classical computers, limiting the scale of feasible simulations. Quantum computing offers a promising way to address these limitations. In this paper, the authors introduce a novel algorithm for pricing American options on quantum hardware. To date, only one method has been proposed for this purpose. The authors' approach combines the Quantum Binomial Tree with Quantum Machine Learning to enable direct valuation of American options on a quantum computer. By incorporating quantum amplitude estimation, it could achieve a quadratic speed-up over classical Monte Carlo methods. Furthermore, it exploits the exponential growth of the quantum state vector, overcoming the memory bottlenecks that restrict classical approaches.