Pricing vulnerable options under cross-asset markov-modulated jump-diffusion dynamics

Yu-Min Lian and Jun-Home Chen

International Review of Economics & Finance, 2024, vol. 94, issue C

Abstract: In this study, the dynamics of the underlying asset price and the counterparty's asset price are governed by a cross-asset Markov-modulated jump-diffusion model that captures the time-inhomogeneity and systematic cojumps. Additionally, the forward interest rate processes are driven by a Markov-modulated Heath–Jarrow–Morton model to depict stochastic volatilities. Under an incomplete-market setting, we apply the Markov-modulated Esscher transform technique to determine a risk-neutral martingale measure. After determining the Markov-modulated Esscher parameters, we obtain an integral expression on the prices of vulnerable European-style Black–Scholes options. The numerical illustrations indicate that the findings are consistent with Klein (1996) and contribute to the extant literature on cojumping impacts on vulnerable option prices.

Keywords: Cross-asset markov-modulated jump-diffusion model; Markov-modulated; Heath–jarrow–morton model; Time-inhomogeneity; Systematic cojump; Markov-modulated esscher transform (search for similar items in EconPapers)
JEL-codes: C15 E32 G01 G12 G13 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:reveco:v:94:y:2024:i:c:s1059056024003848

DOI: 10.1016/j.iref.2024.103392

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