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

Dong An, Noah Linden, Jin-Peng Liu, Ashley Montanaro, Changpeng Shao and Jiasu Wang

Papers from arXiv.org

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.

Date: 2020-12, Revised 2021-06
New Economics Papers: this item is included in nep-cmp and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Quantum 5, 481 (2021)

Downloads: (external link)
http://arxiv.org/pdf/2012.06283 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2012.06283

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().