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 stochastic equations (SDEs). Firstly provide a algorithm that gives quadratic speed-up multilevel Monte Carlo methods general setting. As applications, apply it to compute expectation values determined classical solutions of SDEs, with improved dependence on precision. We demonstrate the use this variety applications arising mathematical finance, such as Black-Scholes Local Volatility models, Greeks. also based sublinear binomial sampling option pricing model same improvement.