Pricing derivatives on foreign assets using Markov-modulated cojump-diffusion dynamics

Yu-Min Lian, Jun-Home Chen and Szu-Lang Liao

International Review of Economics & Finance, 2024, vol. 93, issue PB, 503-519

Abstract: In this study, cross-currency derivatives pricing under stochastic interest rates is analyzed when Markov-modulated cojump-diffusion dynamics with both idiosyncratic and simultaneous jumps drive the underlying foreign equity price and foreign exchange rate processes. More specifically, the noise dynamics of these two assets are captured by the correlated Wiener processes, and the two types of jump events are described as two independent compound Poisson processes with log-normal jump amplitudes. Cojumping addresses the correlation between these two asset price jumps. In an incomplete market setting, the dynamic Esscher transform approach is applied to determine a pricing kernel. According to the resulting dynamics, explicit analytical formulas for evaluating values of European foreign equity call options are provided. Numerical experiments are also described.

Keywords: Cross-currency derivatives; Foreign exchange rate; Simultaneous jump; Markov-modulated cojump-diffusion dynamics; Esscher transform (search for similar items in EconPapers)
JEL-codes: F31 G12 G13 G15 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:reveco:v:93:y:2024:i:pb:p:503-519

DOI: 10.1016/j.iref.2024.04.030

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