IDEAS home Printed from https://ideas.repec.org/a/eee/finlet/v9y2012i3p176-181.html
   My bibliography  Save this article

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

Author

Listed:
  • Hsu, Pao-Peng
  • Chen, Ying-Hsiu

Abstract

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/j.frl.2011.10.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1544612311000456
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.frl.2011.10.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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..
    2. 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.
    3. 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.
    4. Cho-hoi Hui, 2006. "Currency Barrier Option Pricing with Mean Reversion," Working Papers 0605, Hong Kong Monetary Authority.
    5. 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, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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 & 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.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, December.
    2. 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.
    3. Zhanyu Chen & Kai Zhang & Hongbiao Zhao, 2022. "A Skellam market model for loan prime rate options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(3), pages 525-551, March.
    4. Carl Chiarella & Christina Sklibosios, 2003. "A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 10(2), pages 87-127, September.
    5. Carl Chiarella & Christina Nikitopoulos Sklibosios & Erik Schlogl, 2007. "A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton Models with Jumps," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 365-399.
    6. Leo Krippner, 2006. "A Theoretically Consistent Version of the Nelson and Siegel Class of Yield Curve Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 39-59.
    7. Ming-Chieh Wang & Li-Jhang Huang, 2019. "Pricing cross-currency interest rate swaps under the Levy market model," Review of Derivatives Research, Springer, vol. 22(2), pages 329-355, July.
    8. 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.
    9. S. Galluccio & J.‐M. Ly & Z. Huang & O. Scaillet, 2007. "Theory And Calibration Of Swap Market Models," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 111-141, January.
    10. Robert Jarrow & Haitao Li & Feng Zhao, 2007. "Interest Rate Caps “Smile” Too! But Can the LIBOR Market Models Capture the Smile?," Journal of Finance, American Finance Association, vol. 62(1), pages 345-382, February.
    11. Leif Andersen, 2010. "Markov models for commodity futures: theory and practice," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 831-854.
    12. Guan, Lim Kian & Ting, Christopher & Warachka, Mitch, 2005. "The implied jump risk of LIBOR rates," Journal of Banking & Finance, Elsevier, vol. 29(10), pages 2503-2522, October.
    13. 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).
    14. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 6, July-Dece.
    15. 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).
    16. 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.
    17. 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.
    18. L. Steinruecke & R. Zagst & A. Swishchuk, 2015. "The Markov-switching jump diffusion LIBOR market model," Quantitative Finance, Taylor & Francis Journals, vol. 15(3), pages 455-476, March.
    19. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    20. Son-Nan Chen & Pao-Peng Hsu & Chang-Yi Li, 2016. "Pricing credit-risky bonds and spread options modelling credit-spread term structures with two-dimensional Markov-modulated jump-diffusion," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 573-592, April.

    More about this item

    Keywords

    Levy process; Barrier option; HJM;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:finlet:v:9:y:2012:i:3:p:176-181. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/frl .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.