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New developments in econophysics: Option pricing formulas

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  • Moawia Alghalith

Abstract

We synthesize and discuss some new developments in econophysics. In doing so, we focus on option pricing. We relax the assumptions of constant volatility and interest rate. In doing so, we rely on the square root of the Brownian motion. We also provide simple, closed-form pricing formulas for the American and Bermudan options.

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  • Moawia Alghalith, 2023. "New developments in econophysics: Option pricing formulas," Papers 2301.11078, arXiv.org.
    • Handle: RePEc:arx:papers:2301.11078
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    References listed on IDEAS

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    1. Alghalith, Moawia, 2018. "Pricing the American options using the Black–Scholes pricing formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 443-445.
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    3. Alghalith, Moawia, 2020. "Pricing options under simultaneous stochastic volatility and jumps: A simple closed-form formula without numerical/computational methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    5. Frasca, Marco & Farina, Alfonso & Alghalith, Moawia, 2021. "Quantized noncommutative Riemann manifolds and stochastic processes: The theoretical foundations of the square root of Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 577(C).
    6. Alghalith, Moawia, 2020. "Pricing the American options: A closed-form, simple formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    7. 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.
    8. Moawia Alghalith, 2021. "Pricing Options Under Stochastic Interest Rate And The Frasca–Farina Process: A Simple, Explicit Formula," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-4, March.
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