Quantum-inspired variational algorithms for partial differential equations: application to financial derivative pricing

Tianchen Zhao; Chuhao Sun; Asaf Cohen; James Stokes; Shravan Veerapaneni

doi:https://doi.org/10.1080/14697688.2023.2259954

Quantum-inspired variational algorithms for partial differential equations: application to financial derivative pricing

Tianchen Zhao, Chuhao Sun, Asaf Cohen, James Stokes, Shravan Veerapaneni

Research output: Contribution to journal › Article › peer-review

Abstract

Variational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of partial differential equations (PDEs); namely, the real- and imaginary time-dependent Schrödinger equation. In this paper, we present a simple generalization of VMC applicable to arbitrary time-dependent PDEs, showcasing the technique in the multi-asset Black-Scholes PDE for pricing European options contingent on many correlated underlying assets.

Original language	American English
Pages (from-to)	1-11
Number of pages	11
Journal	Quantitative Finance
Volume	24
Issue number	1
DOIs	https://doi.org/10.1080/14697688.2023.2259954
State	Published - 1 Jan 2023
Externally published	Yes

Keywords

Multi-asset Black-Scholes PDE
Variational quantum algorithms
Variational quantum Monte Carlo

All Science Journal Classification (ASJC) codes

Finance
General Economics,Econometrics and Finance
Economics, Econometrics and Finance(all)

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Cite this

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abstract = "Variational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of partial differential equations (PDEs); namely, the real- and imaginary time-dependent Schr{\"o}dinger equation. In this paper, we present a simple generalization of VMC applicable to arbitrary time-dependent PDEs, showcasing the technique in the multi-asset Black-Scholes PDE for pricing European options contingent on many correlated underlying assets.",

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AU - Sun, Chuhao

AU - Cohen, Asaf

AU - Stokes, James

AU - Veerapaneni, Shravan

PY - 2023/1/1

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AB - Variational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of partial differential equations (PDEs); namely, the real- and imaginary time-dependent Schrödinger equation. In this paper, we present a simple generalization of VMC applicable to arbitrary time-dependent PDEs, showcasing the technique in the multi-asset Black-Scholes PDE for pricing European options contingent on many correlated underlying assets.

KW - Multi-asset Black-Scholes PDE

KW - Variational quantum algorithms

KW - Variational quantum Monte Carlo

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JO - Quantitative Finance

JF - Quantitative Finance

IS - 1

ER -

Quantum-inspired variational algorithms for partial differential equations: application to financial derivative pricing

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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