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Asymptotic Estimation of Two Telegraph Particle Collisions and Spread Options Valuations

Author

Listed:
  • Anatoliy A. Pogorui

    (Department of Mathematics, Zhytomyr State University, Valyka Berdychivska St., 40, 10008 Zhytomyr, Ukraine)

  • Anatoliy Swishchuk

    (Department of Mathematics & Statistics, University of Calgary, Calgary, AB T2N 1N4, Canada)

  • Ramón M. Rodríguez-Dagnino

    (School of Engineering and Sciences, Tecnologico de Monterrey, Av. Eugenio Garza Sada 2501 Sur, C.P., Monterrey 64849, Nuevo León, Mexico)

Abstract

In this paper, we study collisions of two telegraph particles on a line that are described by telegraph processes between collisions. We obtain an asymptotic estimation of the number of collisions under Kac’s condition for the cases where the direction-switching processes have the same parameters and different parameters. We also consider the application of these results to evaluate Margrabe’s spread option for two assets of spot prices modeled by two telegraph processes.

Suggested Citation

  • Anatoliy A. Pogorui & Anatoliy Swishchuk & Ramón M. Rodríguez-Dagnino, 2022. "Asymptotic Estimation of Two Telegraph Particle Collisions and Spread Options Valuations," Mathematics, MDPI, vol. 10(13), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2201-:d:846639
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    References listed on IDEAS

    as
    1. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    2. Jaehyuk Choi, 2018. "Sum of all Black–Scholes–Merton models: An efficient pricing method for spread, basket, and Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(6), pages 627-644, June.
    3. Anatoliy A. Pogorui & Anatoliy Swishchuk & Ramón M. Rodríguez-Dagnino, 2021. "Transformations of Telegraph Processes and Their Financial Applications," Risks, MDPI, vol. 9(8), pages 1-21, August.
    4. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
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