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 Schrödinger 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.Date: December 6, 2019. 2010 Mathematics Subject Classification. 35Q40, 91G20, 91G80. Key words and phrases. quantum algorithms, option pricing, PDE, Schrödinger equation. The views and opinions expressed here are the authors' and do not represent the opinions of their employers. They are not responsible for any use that may be made of these contents. No part of this presentation is intended to influence investment decisions or promote any product or service. The authors would like to thank Alexei Kondratyev for stimulating discussions.
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