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

• URL: http://arxiv.org/abs/2012.06283v2
• Date: Tue, 22 Jun 2021 20:22:56 GMT
• Title: Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance
• Authors: Dong An, Noah Linden, Jin-Peng Liu, Ashley Montanaro, Changpeng Shao, Jiasu Wang
• Abstract summary: We study quantum algorithms for differential equations (SDEs) We provide a quantum algorithm that gives a quadratic speed-up for multilevel Monte Carlo methods in a general setting. We demonstrate the use of this algorithm in a variety of applications arising in mathematical finance.
• Score: 1.128265591164748
• License: http://creativecommons.org/licenses/by/4.0/
• 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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