Quantum walk option pricing model based on binary tree

Qi Han and Xuan Song

Physica A: Statistical Mechanics and its Applications, 2025, vol. 658, issue C

Abstract: In this paper, we propose a quantum option pricing model in a risk-neutral framework. We innovatively incorporate quantum walk theory into the binomial tree option pricing model by using probability amplitudes of quantum superposition states instead of classical probabilities in order to simultaneously consider the state of the asset price at multiple nodes. From the perspective of quantum mechanics, we delve into one-step and multi-step quantum binomial tree models and derive the corresponding quantum binomial tree option pricing formulas. The experimental results show that the resulting option prices are very close to those of the classical model, indicating that the quantum model can capture subtle market dynamics while maintaining the classical model’s pricing accuracy.

Keywords: Quantum finance; Quantum walk; Binomial tree model; Option pricing; Risk-neutral (search for similar items in EconPapers)
JEL-codes: D53 G12 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:658:y:2025:i:c:s0378437124007143

DOI: 10.1016/j.physa.2024.130205

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