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The Quantum Black-Scholes Equation

Author

Listed:
  • Luigi Accardi
  • Andreas Boukas

Abstract

Motivated by the work of Segal and Segal on the Black-Scholes pricing formula in the quantum context, we study a quantum extension of the Black-Scholes equation within the context of Hudson-Parthasarathy quantum stochastic calculus. Our model includes stock markets described by quantum Brownian motion and Poisson process.

Suggested Citation

  • Luigi Accardi & Andreas Boukas, 2007. "The Quantum Black-Scholes Equation," Papers 0706.1300, arXiv.org.
    • Handle: RePEc:arx:papers:0706.1300
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    Cited by:

    1. L. Ingber, 2018. "Quantum path integral for financial options," Lester Ingber Papers 18qp, Lester Ingber.
    2. L. Ingber, 2018. "Quantum Variables in Finance and Neuroscience," Lester Ingber Papers 18qv, Lester Ingber.
    3. L. Ingber, 2017. "Quantum Path-Integral qPATHINT Algorithm," Lester Ingber Papers 17qa, Lester Ingber.
    4. Haven, Emmanuel, 2008. "Elementary Quantum Mechanical Principles and Social Science: Is There a Connection?," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 5(1), pages 41-58, March.
    5. L. Ingber, 2016. "Path-integral quantum PATHTREE and PATHINT algorithms," Lester Ingber Papers 16pi, Lester Ingber.
    6. L. Ingber, 2017. "Options on quantum money: Quantum path-integral with serial shocks," Lester Ingber Papers 17oq, Lester Ingber.
    7. L. Ingber, 2022. "Quantum Variables in Finance," Lester Ingber Papers 22qv, Lester Ingber.
    8. L. Ingber, 2017. "Evolution of regenerative Ca-ion wave-packet in neuronal-firing fields: Quantum path-integral with serial shocks," Lester Ingber Papers 17qp, Lester Ingber.
    9. Pineiro-Chousa, Juan & Vizcaíno-González, Marcos, 2016. "A quantum derivation of a reputational risk premium," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 304-309.
    10. Jinge Bao & Patrick Rebentrost, 2022. "Fundamental theorem for quantum asset pricing," Papers 2212.13815, arXiv.org, revised Apr 2023.
    11. L. Ingber, 2021. "Hybrid classical-quantum computing: Applications to statistical mechanics of financial markets," Lester Ingber Papers 21cq, Lester Ingber.
    12. L. Ingber, 2020. "Revisiting Our Quantum World," Lester Ingber Papers 20rq, Lester Ingber.

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