Financial Modelling Based on Telegraph Processes

Nikita Ratanov and Alexander D. Kolesnik
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Nikita Ratanov: Chelyabinsk State University
Alexander D. Kolesnik: Institute of Mathematics and Computer Science

Chapter 7 in Telegraph Processes and Option Pricing, 2022, pp 341-425 from Springer

Abstract: Abstract This last chapter of the book is devoted to financial applications of the previously described results. After brief preliminaries, the chapter opens with some well-known models of the financial market based on jump-telegraph processes. Here the natural interpretation of the concept of volatility is of particular interest. Explicit formulae for pricing of standard options and a fundamental equation are obtained, rounded out by historical and implied volatility formulae. We then examine some financial market models that are based on the classes of processes presented in Chap. 3 : the model with short memory properties, double telegraph, and Poisson-modulated markets are presented. Finally, we look at diffusion-telegraph models, which bridge the gap between the classical Black–Scholes–Merton model based on a Wiener process (with jumps) and the standard jump-telegraph market model presented in the first sections of this chapter.

Date: 2022
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DOI: 10.1007/978-3-662-65827-7_7

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