|Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance
|Year of Publication
|An, D, Linden, N, Liu, J-P, Montanaro, A, Shao, C, Wang, J
|Quantum 5, 481 (2021)
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.