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Financial Modelling Based on Telegraph Processes

In: Telegraph Processes and Option Pricing

Author

Listed:
  • Nikita Ratanov

    (Chelyabinsk State University)

  • Alexander D. Kolesnik

    (Institute of Mathematics and Computer Science)

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.

Suggested Citation

  • Nikita Ratanov & Alexander D. Kolesnik, 2022. "Financial Modelling Based on Telegraph Processes," Springer Books, in: Telegraph Processes and Option Pricing, edition 2, chapter 7, pages 341-425, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-65827-7_7
    DOI: 10.1007/978-3-662-65827-7_7
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