Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance
arXiv:2012.06283 · doi:10.22331/q-2021-06-24-481
Abstract
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.
arXiv comment37 pages, 6 figures
References in corpus (20)
- Quantum algorithm for solving linear systems of equations
- Quantum computing for finance: overview and prospects
- Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
- Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
- Quantum speedup of Monte Carlo methods
- Preconditioned quantum linear system algorithm
- Quantum computational finance: Monte Carlo pricing of financial derivatives
- High-order quantum algorithm for solving linear differential equations
- Efficient quantum algorithm for dissipative nonlinear differential equations
- Option Pricing using Quantum Computers
- Quantum algorithm for linear differential equations with exponentially improved dependence on precision
- Quantum algorithms and the finite element method
- Quantum algorithm and circuit design solving the Poisson equation
- Quantum algorithms for systems of linear equations inspired by adiabatic quantum computing
- High-precision quantum algorithms for partial differential equations
- Quantum Algorithm for Simulating the Wave Equation
- Quantum spectral methods for differential equations
- Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems
- Fast inversion, preconditioned quantum linear system solvers, and fast evaluation of matrix functions
- Quantum Algorithm for the Vlasov Equation
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