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Quantum walk option pricing model based on binary tree

Author

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  • Han, Qi
  • Song, Xuan

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.

Suggested Citation

  • Han, Qi & Song, Xuan, 2025. "Quantum walk option pricing model based on binary tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 658(C).
    • Handle: RePEc:eee:phsmap:v:658:y:2025:i:c:s0378437124007143
    DOI: 10.1016/j.physa.2024.130205
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    References listed on IDEAS

    as
    1. Sarkissian, Jack, 2020. "Quantum coupled-wave theory of price formation in financial markets: Price measurement, dynamics and ergodicity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    2. Jack Sarkissian, 2020. "Quantum coupled-wave theory of price formation in financial markets: price measurement, dynamics and ergodicity," Papers 2002.04212, arXiv.org.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    4. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Quantum finance; Quantum walk; Binomial tree model; Option pricing; Risk-neutral;
    All these keywords.

    JEL classification:

    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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