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Pricing Currency Derivatives with Markov-modulated Levy Dynamics

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  • Anatoliy Swishchuk
  • Maksym Tertychnyi
  • Robert Elliott

Abstract

Using a Levy process we generalize formulas in Bo et al.(2010) for the Esscher transform parameters for the log-normal distribution which ensure the martingale condition holds for the discounted foreign exchange rate. Using these values of the parameters we find a risk-neural measure and provide new formulas for the distribution of jumps, the mean jump size, and the Poisson process intensity with respect to to this measure. The formulas for a European call foreign exchange option are also derived. We apply these formulas to the case of the log-double exponential distribution of jumps. We provide numerical simulations for the European call foreign exchange option prices with different parameters.

Suggested Citation

  • Anatoliy Swishchuk & Maksym Tertychnyi & Robert Elliott, 2014. "Pricing Currency Derivatives with Markov-modulated Levy Dynamics," Papers 1402.1953, arXiv.org.
    • Handle: RePEc:arx:papers:1402.1953
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    Cited by:

    1. Milan Kumar Das & Anindya Goswami, 2019. "Testing of binary regime switching models using squeeze duration analysis," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-20, March.
    2. Wenhan Li & Cuixiang Li & Lixia Liu & Mengna Wang, 2021. "Foreign Currency Power Option Pricing Based on Esscher Transform," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 535-548, August.
    3. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2017. "Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 46-62.
    4. Lian, Yu-Min & Chen, Jun-Home & Liao, Szu-Lang, 2016. "Option pricing on foreign exchange in a Markov-modulated, incomplete-market economy," Finance Research Letters, Elsevier, vol. 16(C), pages 208-219.
    5. Lian, Yu-Min & Chen, Jun-Home, 2022. "Foreign exchange option pricing under regime switching with asymmetrical jumps," Finance Research Letters, Elsevier, vol. 46(PA).
    6. Bo, Lijun & Tang, Dan & Wang, Yongjin, 2017. "Optimal investment of variance-swaps in jump-diffusion market with regime-switching," Journal of Economic Dynamics and Control, Elsevier, vol. 83(C), pages 175-197.
    7. 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).
    8. Milan Kumar Das & Anindya Goswami, 2018. "Testing of Binary Regime Switching Models using Squeeze Duration Analysis," Papers 1807.04393, arXiv.org, revised Aug 2018.
    9. 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.
    10. Lian, Yu-Min & Chen, Jun-Home, 2023. "Valuation of chooser options with state-dependent risks," Finance Research Letters, Elsevier, vol. 52(C).
    11. David Liu, 2020. "Markov modulated jump-diffusions for currency options when regime switching risk is priced," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 1-26, February.

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