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The Black–Scholes equation in finance: Quantum mechanical approaches

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  • Yeşiltaş, Özlem

Abstract

In this paper, the Black–Scholes equation of the option pricing theory in order to minimize the risk through the stocks is studied. The solutions are obtained in terms of exceptional Laguerre polynomials. Moreover, higher-order supesymmetric representations are studied with a special case of third order. The Darboux transformation of the heat equation linked to the Black–Scholes system is given and a new potential is shown.

Suggested Citation

  • Yeşiltaş, Özlem, 2023. "The Black–Scholes equation in finance: Quantum mechanical approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 623(C).
    • Handle: RePEc:eee:phsmap:v:623:y:2023:i:c:s0378437123004648
    DOI: 10.1016/j.physa.2023.128909
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    References listed on IDEAS

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    1. Jana, T.K. & Roy, P., 2011. "Supersymmetry in option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2350-2355.
    2. Viktor Stojkoski & Trifce Sandev & Lasko Basnarkov & Ljupco Kocarev & Ralf Metzler, 2020. "Generalised geometric Brownian motion: Theory and applications to option pricing," Papers 2011.00312, arXiv.org.
    3. Nasser Saad & Richard L. Hall & Hakan Çiftçi & Özlem Yeşiltaş, 2011. "Study of the Generalized Quantum Isotonic Nonlinear Oscillator Potential," Advances in Mathematical Physics, Hindawi, vol. 2011, pages 1-20, June.
    4. Will Hicks, 2019. "Closed Quantum Black-Scholes: Quantum Drift and the Heisenberg Equation of Motion," Papers 1911.11475, arXiv.org, revised Jan 2020.
    5. Contreras, M. & Echeverría, J. & Peña, J.P. & Villena, M., 2020. "Resonance phenomena in option pricing with arbitrage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    Full references (including those not matched with items on IDEAS)

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    Keywords

    Quantum finance; Black–Scholes model;

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