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Currency barrier option pricing with mean reversion

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  • C. H. Hui
  • C. F. Lo

Abstract

This article develops a barrier option pricing model in which the exchange rate follows a mean‐reverting lognormal process. The corresponding closed‐form solutions for the barrier options with time‐dependent barriers are derived. The numerical results show that barrier option values and the corresponding hedge parameters under the proposed model are different from those based on the Black‐Scholes model. For an up‐and‐out call, the mean‐reverting process keeps the exchange rate in a small range around the mean level. When the mean level is below the barrier but above the strike price, the risk of the call to be knocked out is reduced and its option value is enhanced compared with the value under the Black‐Scholes model. The parameters of the mean‐reverting lognormal process therefore have a material impact on the valuation of currency barrier options and their hedge parameters. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:939–958, 2006

Suggested Citation

  • C. H. Hui & C. F. Lo, 2006. "Currency barrier option pricing with mean reversion," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 26(10), pages 939-958, October.
    • Handle: RePEc:wly:jfutmk:v:26:y:2006:i:10:p:939-958
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    Cited by:

    1. Chiu, Hsin-Yu & Chen, Ting-Fu, 2020. "Impact of volatility jumps in a mean-reverting model: Derivative pricing and empirical evidence," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    2. Zhong, Yinhui & Bao, Qunfang & Li, Shenghong, 2015. "FX options pricing in logarithmic mean-reversion jump-diffusion model with stochastic volatility," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 1-13.
    3. Jeon, Junkee & Kim, Geonwoo, 2022. "Pricing European continuous-installment currency options with mean-reversion," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    4. Chen, Son-Nan & Hsu, Pao-Peng, 2018. "Pricing and hedging barrier options under a Markov-modulated double exponential jump diffusion-CIR model," International Review of Economics & Finance, Elsevier, vol. 56(C), pages 330-346.
    5. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, October.
    6. Junkee Jeon & Geonwoo Kim, 2022. "Analytic Valuation Formula for American Strangle Option in the Mean-Reversion Environment," Mathematics, MDPI, vol. 10(15), pages 1-19, July.
    7. Wong, Hoi Ying & Lo, Yu Wai, 2009. "Option pricing with mean reversion and stochastic volatility," European Journal of Operational Research, Elsevier, vol. 197(1), pages 179-187, August.
    8. Hsu, Pao-Peng & Chen, Ying-Hsiu, 2012. "Barrier option pricing for exchange rates under the Levy–HJM processes," Finance Research Letters, Elsevier, vol. 9(3), pages 176-181.

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