A Quantum Walk Model of Financial Options
Orrell D (2020) Quantum Economics and Finance: An Applied Mathematics Introduction. Panda Ohana Publishing.
Posted: 17 Jan 2020 Last revised: 10 Dec 2020
Date Written: January 1, 2020
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.
Keywords: financial options, quantum walk, quantum finance, quantum cognition, quantum computing
JEL Classification: C01, G10
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