The Pricing of American Options on the Quantum Computer at SSRN
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.
In the paper, I propose a new effective approach to the probability distribution loading for derivative pricing. The Quantum Binomial Tree Model is the quantum implementation of the classical Binomial Tree, and through the use of quantum computing properties, we have a large improvement in complexity compared to the classical method. This method allows us to increase the number of Monte Carlo paths exponentially on a quantum computer. I demonstrate the introduced technique for option pricing with a time dependent volatility and I show how the model can be extended to use local volatility. I also conduct the complexity analysis.
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