A Quantum Walk Model of Financial Options

Abstract

Financial markets are often modeled using a random walk, for example in the binomial option pricing model which is a discrete version of the Black-Scholes formula. This paper presents an alternative approach to option pricing based on a quantum walk model. The quantum walk, which incorporates superposition states and allows for effects such as interference, was originally developed in physics, but has also seen application in areas such as cognitive psychology, where it is used to model dynamic decision-making processes. It is shown here that the quantum walk model captures key aspects of investor behavior, while the collapsed state captures the observed behavior of markets. The resulting option price model agrees quite closely with the classical random walk model, but helps to explain some observed anomalies. The method also has the advantage that it can be run directly on a quantum computer. The aim of this paper is to initiate a discussion about how non-classical models that are native to quantum computers can be applied in finance.

Keywords: financial options, quantum walk, quantum finance, quantum cognition, quantum computing

JEL Classification: C01, G10