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Computation of the unknown volatility from integral option price observations in jump–diffusion models

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  • Georgiev, Slavi G.
  • Vulkov, Lubin G.

Abstract

In this work we propose a simple and efficient algorithm to numerically approximate the time-dependent implied volatility for jump–diffusion models in option pricing that generalize the Black–Scholes equation. Here we use implicit–explicit difference schemes to compute the derivative part with fully implicit method and the integral term — in an explicit way. An average in time linearization of the diffusion term is applied, followed by a special decomposition of the unknown volatility function, which enables us to derive the implied volatility in an explicit form. Furthermore, the correctness of the algorithms is established. The presented numerical simulations demonstrate the capabilities of the current approach and confirm the robustness of the proposed methodology.

Suggested Citation

  • Georgiev, Slavi G. & Vulkov, Lubin G., 2021. "Computation of the unknown volatility from integral option price observations in jump–diffusion models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 591-608.
    • Handle: RePEc:eee:matcom:v:188:y:2021:i:c:p:591-608
    DOI: 10.1016/j.matcom.2021.05.008
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    References listed on IDEAS

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    1. Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October.
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    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    4. Vinicius V. L. Albani & Jorge P. Zubelli, 2020. "A splitting strategy for the calibration of jump-diffusion models," Finance and Stochastics, Springer, vol. 24(3), pages 677-722, July.
    5. Egorova, Yana, 2017. "Инвестирование Денежных Средств В Условиях Экономического Кризиса В 2017 Году," MPRA Paper 77648, University Library of Munich, Germany.
    6. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    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.
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    Cited by:

    1. Sun, Fengrui & Liu, Dameng & Cai, Yidong & Qiu, Yongkai, 2023. "Surface jump mechanism of gas molecules in strong adsorption field of coalbed methane reservoirs," Applied Energy, Elsevier, vol. 349(C).

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