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arXiv · 2012.06283

Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance

Dong An·Noah Linden·Jin-Peng Liu·Ashley Montanaro·Changpeng Shao·Jiasu Wang
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Abstract

Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study quantum algorithms for stochastic differential equations (SDEs). Firstly we provide a quantum algorithm that gives a quadratic speed-up for multilevel Monte Carlo methods in a general setting. As applications, we apply it to compute expectation values determined by classical solutions of SDEs, with improved dependence on precision. We demonstrate the use of this algorithm in a variety of applications arising in mathematical finance, such as the Black-Scholes and Local Volatility models, and Greeks. We also provide a quantum algorithm based on sublinear binomial sampling for the binomial option pricing model with the same improvement.

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Dong An, Noah Linden, Jin-Peng Liu, Ashley Montanaro, Changpeng Shao, Jiasu Wang. 2021-06-22. Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance. https://doi.org/10.22331/q-2021-06-24-481

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