On Barrier Binary Options in the Telegraph-like Financial Market Model

Abstract

The article continues the study of the market model based on jump-telegraph processes. It is assumed that the price of a risky asset follows the stochastic exponential of a piecewise linear process, equipped with jumps that occur at the moments of a pattern change. In this case, the standard option pricing formula was derived previously, while exotic options for this model have not yet been explored. Within this framework, we are developing procedures for pricing binary barrier options. This article concerns the “cash-(at hit)-or-nothing” binary barrier option. The main tools of this analysis are methods developed for first-pass probabilities. Some known results related to the ruin probabilities follow directly from these settings.

Keywords

• piecewise deterministic stochastic process
• jump-telegraph process
• martingales
• binary option
• barrier option