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The pricing of foreign currency options under jump‐diffusion processes

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  • Chang Mo Ahn
  • D. Chinhyung Cho
  • Keehwan Park

Abstract

In this article, the authors derive explicit formulas for European foreign exchange (FX) call and put option values when the exchange rate dynamics are governed by jump‐diffusion processes. The authors use a simple general equilibrium international asset pricing model with continuous trading and frictionless international capital markets. The domestic and foreign price level are introduced as state variables that contain jumps caused by monetary shocks and catastrophic events such as 9/11 or Hurricane Katrina. The domestic and foreign interest rates are stochastic and endogenously determined in the model and are shown to be critically affected by the jump risk of the foreign exchange. The model shows that the behavior of FX options is affected through the impact of state variables and parameters on the nominal interest rates. The model contrasts with those of M. Garman and S. Kohlhagen (1983) and O. Grabbe (1983), whose models have exogenously determined interest rates. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:669–695, 2007

Suggested Citation

  • Chang Mo Ahn & D. Chinhyung Cho & Keehwan Park, 2007. "The pricing of foreign currency options under jump‐diffusion processes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 27(7), pages 669-695, July.
    • Handle: RePEc:wly:jfutmk:v:27:y:2007:i:7:p:669-695
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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).
    2. 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.
    3. Sandun Perera & Winston Buckley & Hongwei Long, 2018. "Market-reaction-adjusted optimal central bank intervention policy in a forex market with jumps," Annals of Operations Research, Springer, vol. 262(1), pages 213-238, March.
    4. Mohammad Abedi & Daniel Bartolomeo, 2019. "Entropic Dynamics of Exchange Rates and Options," Papers 1908.06358, arXiv.org.
    5. Yang, Chih-Yuan & Jhang, Ling-Jhen & Chang, Chia-Chien, 2016. "Do investor sentiment, weather and catastrophe effects improve hedging performance? Evidence from the Taiwan options market," Pacific-Basin Finance Journal, Elsevier, vol. 37(C), pages 35-51.
    6. Lin, Shih-Kuei & Wang, Shin-Yun & Chen, Carl R. & Xu, Lian-Wen, 2017. "Pricing Range Accrual Interest Rate Swap employing LIBOR market models with jump risks," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 359-373.
    7. Chuang, Ming-Che & Wen, Chin-Hsiang & Lin, Shih-Kuei, 2020. "Valuation and empirical analysis of currency options," International Review of Economics & Finance, Elsevier, vol. 66(C), pages 71-91.
    8. 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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