Asymptotic Estimation of Two Telegraph Particle Collisions and Spread Options Valuations

Pogorui, A. A.; Swishchuk, Anatoliy; Rodríguez‐Dagnino, Ramón M.

doi:10.3390/math10132201

Cited by 1 publication

(2 citation statements)

References 14 publications

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“…Moreover, in a trading market structure having high-frequency behavior, our telegraph process model for stock price results is more descriptive than the Black-Scholes model. See our paper for further details (Pogorui et al (2022)).…”

Section: Numerical Example 2 (Black-scholes Formula Based On Example 3)mentioning

confidence: 97%

“…Some finite-velocity random motions driven by the geometric counting process were studied in Di Crescenzo et al (2023). Symmetrical and asymmetrical classical telegraph processes and their applications in option pricing and spread option valuations were considered in Pogorui et al (2021aPogorui et al ( , 2021bPogorui et al ( , 2021cPogorui et al ( , 2022.…”

Section: Introductionmentioning

confidence: 99%

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Cox-Based and Elliptical Telegraph Processes and Their Applications

Pogorui

Swishchuk

Rodríguez‐Dagnino

et al. 2023

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This paper studies two new models for a telegraph process: Cox-based and elliptical telegraph processes. The paper deals with the stochastic motion of a particle on a straight line and on an ellipse with random positive velocity and two opposite directions of motion, which is governed by a telegraph–Cox switching process. A relevant result of our analysis on the straight line is obtaining a linear Volterra integral equation of the first kind for the characteristic function of the probability density function (PDF) of the particle position at a given time. We also generalize Kac’s condition for the telegraph process to the case of a telegraph–Cox switching process. We show some examples of random velocity where the distribution of the coordinate of a particle is expressed explicitly. In addition, we present some novel results related to the switched movement evolution of a particle according to a telegraph–Cox process on an ellipse. Numerical examples and applications are presented for a telegraph–Cox-based process (option pricing formulas) and elliptical telegraph process.

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Section: Numerical Example 2 (Black-scholes Formula Based On Example 3)mentioning

confidence: 97%