Asymptotic Estimation of Two Telegraph Particle Collisions and Spread Options Valuations

Anatoliy A. Pogorui, Anatoliy Swishchuk and Ramón M. Rodríguez-Dagnino
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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

Mathematics, 2022, vol. 10, issue 13, 1-14

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.

Keywords: telegraph process; Markov stochastic evolution; collision number; Kac’s condition; Laplace transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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