01351nas a2200193 4500008004100000245011700041210006900158260001400227300000800241490000600249520075900255100001301014700001701027700001801044700002201062700002001084700001601104856003701120 2021 eng d00aQuantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance0 aQuantumaccelerated multilevel Monte Carlo methods for stochastic c6/22/2021 a4810 v53 a
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.
1 aAn, Dong1 aLinden, Noah1 aLiu, Jin-Peng1 aMontanaro, Ashley1 aShao, Changpeng1 aWang, Jiasu uhttps://arxiv.org/abs/2012.06283