Transformations of telegraph processes and their financial applications

Artikel

In this paper, we consider non-linear transformations of classical telegraph process. The main results consist of deriving a general partial differential Equation (PDE) for the probability density (pdf) of the transformed telegraph process, and then presenting the limiting PDE under Kac's conditions, which may be interpreted as the equation for a diffusion process on a circle. This general case includes, for example, classical cases, such as limiting diffusion and geometric Brownian motion under some specifications of non-linear transformations (i.e., linear, exponential, etc.). We also give three applications of non-linear transformed telegraph process in finance: (1) application of classical telegraph process in the case of balance, (2) application of classical telegraph process in the case of dis-balance, and (3) application of asymmetric telegraph process. For these three cases, we present European call and put option prices. The novelty of the paper consists of new results for non-linear transformed classical telegraph process, new models for stock prices based on transformed telegraph process, and new applications of these models to option pricing.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Journal: Risks ; ISSN: 2227-9091 ; Volume: 9 ; Year: 2021 ; Issue: 8 ; Pages: 1-21 ; Basel: MDPI

Klassifikation und Themen

• Klassifikation: Wirtschaft
• Thema: asymmetric telegraph equation ; Black-Scholes formula ; classical telegraph equation ; European call and put options ; transformations of telegraph equation

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Pogorui, Anatoliy A. ; Sviščuk, Anatolij ; Rodríguez-Dagnino, Ramón M.
• Ereignis: Veröffentlichung
• (wer): MDPI
• (wo): Basel
• (wann): 2021

Weitere Informationen

• DOI: doi:10.3390/risks9080147
• Handle: http://hdl.handle.net/10419/258231
• Letzte Aktualisierung: 10.03.2025, 11:42 MEZ