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Barrier option pricing for exchange rates under the Levy–HJM processes


  • Hsu, Pao-Peng
  • Chen, Ying-Hsiu


In this paper, we present closed-forms for the valuation of the barrier option whose underlying is exchange rate under the multi-dimensional Levy process, including stochastic interest rates and stochastic assets. Instantaneous forward interest rates are assumed under the Heath et al. [1992. Econometrica 60, 77–105] framework, and the analytic formulas of the exchange rate barrier option are obtained when the Levy process is restricted in a double exponential process.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:finlet:v:9:y:2012:i:3:p:176-181
    DOI: 10.1016/

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    References listed on IDEAS

    1. 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.
    2. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    3. Johnson, Gordon & Schneeweis, Thomas, 1994. "Jump-Diffusion Processes in the Foreign Exchange Markets and the Release of Macroeconomic News," Computational Economics, Springer;Society for Computational Economics, vol. 7(4), pages 309-329.
    4. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410.
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    Cited by:

    1. Xiao, Shuang & Ma, Shihua, 2016. "Pricing discrete double barrier options under Lévy processes: An extension of the method by Milev and Tagliani," Finance Research Letters, Elsevier, vol. 19(C), pages 67-74.
    2. Chen, Son-Nan & Chiang, Mi-Hsiu & Hsu, Pao-Peng & Li, Chang-Yi, 2014. "Valuation of quanto options in a Markovian regime-switching market: A Markov-modulated Gaussian HJM model," Finance Research Letters, Elsevier, vol. 11(2), pages 161-172.

    More about this item


    Levy process; Barrier option; HJM;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


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