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A Black-Scholes Schrödinger option price: ‘bit’ versus ‘qubit’

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  • Haven, Emmanuel

Abstract

The celebrated Black-Scholes differential equation provides for the price of a financial derivative. The uncertainty environment of such option price can be described by the classical ‘bit’: a system with two possible states. This paper argues for the introduction of a different uncertainty environment characterized by the so called ‘qubit’. We obtain an information-based option price and discuss the differences between this option price and the classical option price.

Suggested Citation

  • Haven, Emmanuel, 2003. "A Black-Scholes Schrödinger option price: ‘bit’ versus ‘qubit’," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 201-206.
    • Handle: RePEc:eee:phsmap:v:324:y:2003:i:1:p:201-206
    DOI: 10.1016/S0378-4371(02)01846-0
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    References listed on IDEAS

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    1. K. J. Arrow, 1964. "The Role of Securities in the Optimal Allocation of Risk-bearing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 31(2), pages 91-96.
    2. 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.
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    Cited by:

    1. Khrennikov, Andrei, 2008. "Quantum-like microeconomics: Statistical model of distribution of investments and production," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5826-5843.
    2. Choustova, Olga Al., 2007. "Quantum Bohmian model for financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 304-314.
    3. Will Hicks, 2020. "Pseudo-Hermiticity, Martingale Processes and Non-Arbitrage Pricing," Papers 2009.00360, arXiv.org, revised Apr 2021.
    4. Bustamante, M. & Contreras, M., 2016. "Multi-asset Black–Scholes model as a variable second class constrained dynamical system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 540-572.
    5. Contreras, Mauricio & Pellicer, Rely & Villena, Marcelo, 2017. "Dynamic optimization and its relation to classical and quantum constrained systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 12-25.
    6. G., Mauricio Contreras & Peña, Juan Pablo, 2019. "The quantum dark side of the optimal control theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 450-473.
    7. Reaz Chowdhury & M. R. C. Mahdy & Tanisha Nourin Alam & Golam Dastegir Al Quaderi, 2018. "Predicting the Stock Price of Frontier Markets Using Modified Black-Scholes Option Pricing Model and Machine Learning," Papers 1812.10619, arXiv.org.
    8. Will Hicks, 2018. "PT Symmetry, Non-Gaussian Path Integrals, and the Quantum Black-Scholes Equation," Papers 1812.00839, arXiv.org, revised Jan 2019.
    9. Contreras, Mauricio & Pellicer, Rely & Villena, Marcelo & Ruiz, Aaron, 2010. "A quantum model of option pricing: When Black–Scholes meets Schrödinger and its semi-classical limit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5447-5459.
    10. Rotundo, Giulia, 2014. "Black–Scholes–Schrödinger–Zipf–Mandelbrot model framework for improving a study of the coauthor core score," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 296-301.
    11. 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.

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