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Joint dynamic modeling and option pricing in incomplete derivative-security market |
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| Affiliation: | 1. Department of Business Administration, Fu Jen Catholic University, No. 510, Zhongzheng Rd., Xinzhuang Dist., New Taipei City 24205, Taiwan;2. Department of Business Administration, National Chin-Yi University of Technology, No. 57, Sec. 2, Zhongshan Rd., Taiping Dist., Taichung 41170, Taiwan;1. Department of Tourism and Hospitality, TransWorld University, No. 1221, Zhennan Rd., Douliu City, Yunlin County 640, Taiwan;2. Department of Economics, Soochow University, No. 56, Kueiyang Street, Section 1, Taipei 100, Taiwan;1. Department of Banking and Finance, Cheng Shiu University, Kaohsiung, Taiwan, ROC;2. Department of Finance, National Kaohsiung University of Science and Technology, Kaohsiung, Taiwan, ROC;3. Sales department, Paralink Networks, Inc., New Taipei City, Taiwan, ROC |
| 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 |
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