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

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.

Automated summary

Inspired by recent progress in quantum algorithms for differential equations, this study focuses on stochastic differential equations (SDEs) and provides a quantum algorithm that improves the efficiency of multilevel Monte Carlo methods. Applications include computing expectation values of SDEs with increased precision in mathematical finance models, such as Black-Scholes and Local Volatility, using the same quantum algorithm for binomial option pricing models with improved performance.