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

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  • Lian, Yu-Min
  • Chen, Jun-Home

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.

Suggested Citation

  • Lian, Yu-Min & Chen, Jun-Home, 2020. "Joint dynamic modeling and option pricing in incomplete derivative-security market," The North American Journal of Economics and Finance, Elsevier, vol. 51(C).
    • Handle: RePEc:eee:ecofin:v:51:y:2020:i:c:s106294081730325x
    DOI: 10.1016/j.najef.2018.09.003
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    Cited by:

    1. Lian, Yu-Min & Chen, Jun-Home, 2022. "Foreign exchange option pricing under regime switching with asymmetrical jumps," Finance Research Letters, Elsevier, vol. 46(PA).
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    3. Lian, Yu-Min & Chen, Jun-Home, 2021. "Pricing virtual currency-linked derivatives with time-inhomogeneity," International Review of Economics & Finance, Elsevier, vol. 71(C), pages 424-439.

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    More about this item

    Keywords

    Joint dynamic modeling; Correlated bivariate Markov-modulated; Geometric Brownian motion model with jump risks; Cojump; Gerber–Siu’s approach;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G01 - Financial Economics - - General - - - Financial Crises
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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