Joint dynamic modeling and option pricing in incomplete derivative-security market

Yu-Min Lian and Jun-Home Chen

The North American Journal of Economics and Finance, 2020, vol. 51, issue C

Abstract: In this study, we evaluate the option prices on two assets under stochastic interest rates when the stochastic process that underlying asset prices follow is depending on a correlated bivariate Markov-modulated geometric Brownian motion model with jump risks. More specifically, we conduct the joint dynamic modeling by identifying two independent compound Poisson processes with the log-normal jump sizes to describe both individual jumps and systematic cojumps. Facilitating the cojumping behavior this way with the time-inhomogeneity of the volatility, option pricing expressions are readily obtainable since the Gerber–Siu’s approach is employed to determine a pricing kernel. The empirical results and numerical illustrations are provided to show the impact of cojumps and stochastic volatilities on option prices.

Keywords: Joint dynamic modeling; Correlated bivariate Markov-modulated; Geometric Brownian motion model with jump risks; Cojump; Gerber–Siu’s approach (search for similar items in EconPapers)
JEL-codes: C15 C63 G01 G13 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecofin:v:51:y:2020:i:c:s106294081730325x

DOI: 10.1016/j.najef.2018.09.003

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