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Pricing options under simultaneous stochastic volatility and jumps: A simple closed-form formula without numerical/computational methods

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  • Alghalith, Moawia

Abstract

We overcome the limitations of the previous literature in the European options pricing. In doing so, we provide a closed-form formula that does not require any numerical/computational methods. The formula is as simple as the classical Black–Scholes pricing formula. In addition, we simultaneously include jumps and stochastic volatility. Our approach implies the introduction of a new class of stochastic processes that are based on Clifford algebras. The approach can be easily generalized to higher dimensional problems.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119317492
    DOI: 10.1016/j.physa.2019.123100
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    References listed on IDEAS

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    1. Zhang, Li-Hua & Zhang, Wei-Guo & Xu, Wei-Jun & Xiao, Wei-Lin, 2012. "The double exponential jump diffusion model for pricing European options under fuzzy environments," Economic Modelling, Elsevier, vol. 29(3), pages 780-786.
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    Cited by:

    1. Moawia Alghalith, 2023. "New developments in econophysics: Option pricing formulas," Papers 2301.11078, arXiv.org.
    2. 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).

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