TY - JOUR T1 - Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance JF - Quantum 5, 481 (2021) Y1 - 2021 A1 - Dong An A1 - Noah Linden A1 - Jin-Peng Liu A1 - Ashley Montanaro A1 - Changpeng Shao A1 - Jiasu Wang AB -

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 expection 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.

VL - 5 U4 - 481 UR - https://arxiv.org/abs/2012.06283 U5 - https://doi.org/10.22331/q-2021-06-24-481 ER -