Jump-Telegraph Market Model: Barrier Binary Options

Nikita Ratanov ()
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Nikita Ratanov: Chelyabinsk State University

A chapter in Mathematical and Statistical Methods for Actuarial Sciences and Finance, 2022, pp 390-396 from Springer

Abstract: Abstract The paper continues the study of a 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 earlier and it is very similar to the classic Black-Scholes formula, see [7]. Meanwhile, exotic options for this model have not been studied yet. 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 cases “down-and-in” and “up-and-in” are studied separately. 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. On the same basis, some advanced versions of binary options can also be developed and studied.

Keywords: Jump-telegraph process; Martingales; Binary option; Barrier option (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-99638-3_63

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DOI: 10.1007/978-3-030-99638-3_63

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