Asymptotic Estimation of Two Telegraph Particle Collisions and Spread Options Valuations

Abstract

In this paper, we study collisions of two telegraph particles on a line that are described by telegraph processes between collisions. We obtain an asymptotic estimation of the number of collisions under Kac’s condition for the cases where the direction-switching processes have the same parameters and different parameters. We also consider the application of these results to evaluate Margrabe’s spread option for two assets of spot prices modeled by two telegraph processes.

Keywords

• telegraph process
• Markov stochastic evolution
• collision number
• Kac’s condition
• Laplace transform