A Quantum Algorithm for Linear PDEs Arising in Finance

15 Pages Posted: 26 Dec 2019

See all articles by Filipe Fontanela

Filipe Fontanela

Lloyds Banking Group

Antoine (Jack) Jacquier

Imperial College London; The Alan Turing Institute

Mugad Oumgari

Lloyds Banking Group

Date Written: December 5, 2019

Abstract

We propose a hybrid quantum-classical algorithm, originated from quantum chemistry, to price European and Asian options in the Black-Scholes model. Our approach is based on the equivalence between the pricing partial differential equation and the Schrodinger equation in imaginary time. We devise a strategy to build a shallow quantum circuit approximation to this equation, only requiring few qubits. This constitutes a promising candidate for the application of Quantum Computing techniques (with large number of qubits affected by noise) in Quantitative Finance.

Keywords: quantum algorithms, option pricing, PDE, Schrodinger equation

JEL Classification: Q40, G20, G80

Suggested Citation

Fontanela, Filipe and Jacquier, Antoine and Oumgari, Mugad, A Quantum Algorithm for Linear PDEs Arising in Finance (December 5, 2019). Available at SSRN: https://ssrn.com/abstract=3499134 or http://dx.doi.org/10.2139/ssrn.3499134

Filipe Fontanela

Lloyds Banking Group ( email )

10 Gresham Street
London, EC2V 7AE
United Kingdom

Antoine Jacquier (Contact Author)

Imperial College London ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://wwwf.imperial.ac.uk/~ajacquie/

The Alan Turing Institute ( email )

British Library, 96 Euston Road
London, NW12DB
United Kingdom

Mugad Oumgari

Lloyds Banking Group ( email )

10 Gresham Street
London, EC2V 7AE
United Kingdom

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