Piecewise linear processes with Poisson-modulated exponential switching times

2021/03/11 by Antonio Di Crescenzo, Barbara Martinucci, Di Crescenzo, Antonio +3
Economics, Econometrics and Finance · Biochemistry, Genetics and Molecular Biology · Mathematics · #Stochastic processes and financial applications #Diffusion and Search Dynamics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2103.06680

Abstract

We consider the jump telegraph process when switching intensities depend on external shocks also accompanying with jumps. The incomplete financial market model based on this process is studied. The Esscher transform, which changes only unobservable parameters, is considered in detail. The financial market model based on this transform can price switching risks as well as jump risks of the model.

Related

• On Financial Markets Based on Telegraph Processes
• Option Pricing Model Based on a Markov-modulated Diffusion with Jumps
• Jump-telegraph models for the short rate: pricing and convexity adjustments of zero coupon bonds
• The first passage time problem for mixed-exponential jump processes with applications in insurance and finance
• Jump Identification as a Proxy of Information Shocks, In Tehran Stock Exchange.