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Valuing foreign currency options with a mean-reverting process: a study of Hong Kong dollar

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  • C. H. Hui

    (Research Department, Hong Kong Monetary Authority, Two International Finance Centre, Central, Hong Kong, China)

  • C. F. Lo

    (Institute of Theoretical Physics and Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China)

  • V. Yeung

    (Research Department, Hong Kong Monetary Authority, Two International Finance Centre, Central, Hong Kong, China)

  • L. Fung

    (Research Department, Hong Kong Monetary Authority, Two International Finance Centre, Central, Hong Kong, China)

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    Abstract

    The theoretical prediction on targeted exchange rates expects mean reversion of the exchange rates. There is some empirical evidence to support this prediction. This paper presents a model for valuing European foreign exchange options in which the forward foreign exchange rate follows a mean-reverting lognormal process. The corresponding closed-form solutions for the option valuation are derived. The mean-reverting process has material impact on the foreign exchange rate option values and their hedge parameters. This tends to decrease the value of a simple put or call. On the other hand, the process also keeps the exchange rate in a small range around the mean level. As this is the region in which an option's intrinsic value is high because of the level of its strike price, there is also a tendency for option values to be enhanced compared with the values of the Black-Scholes model. The numerical results using the forward exchange rates of the Hong Kong dollar and market data of their options show that both of these effects are important for the realistic choices of parameter values. As the dynamics of targeted exchange rates may not follow the standard lognormal process as described by the Black-Scholes model, the mean-reverting option-pricing model may be considered for the valuation of options and estimation of associated hedge parameters on targeted exchange rates. Copyright © 2007 John Wiley & Sons, Ltd.

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    File URL: http://hdl.handle.net/10.1002/ijfe.346
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    Bibliographic Info

    Article provided by John Wiley & Sons, Ltd. in its journal International Journal of Finance & Economics.

    Volume (Year): 13 (2008)
    Issue (Month): 1 ()
    Pages: 118-134

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    Handle: RePEc:ijf:ijfiec:v:13:y:2008:i:1:p:118-134

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    Web page: http://www.interscience.wiley.com/jpages/1076-9307/

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    1. Angelos Kanas, 1998. "Testing for a unit root in ERM exchange rates in the presence of structural breaks: evidence from the bootstrap," Applied Economics Letters, Taylor & Francis Journals, vol. 5(7), pages 407-410.
    2. Anthony, Myrvin & MacDonald, Ronald, 1999. "The width of the band and exchange rate mean-reversion: some further ERM-based results," Journal of International Money and Finance, Elsevier, vol. 18(3), pages 411-428.
    3. Rose, Andrew K. & Svensson, Lars E. O., 1994. "European exchange rate credibility before the fall," European Economic Review, Elsevier, vol. 38(6), pages 1185-1216, June.
    4. Ball, Clifford A. & Roma, Antonio, 1994. "Target zone modelling and estimation for European Monetary System exchange rates," Journal of Empirical Finance, Elsevier, vol. 1(3-4), pages 385-420, July.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    6. Krugman, Paul R, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, MIT Press, vol. 106(3), pages 669-82, August.
    7. Paul Soderlind & Lars E. O. Svensson, 1997. "New Techniques to Extract Market Expectations from Financial Instruments," NBER Working Papers 5877, National Bureau of Economic Research, Inc.
    8. Anthony, Myrvin & MacDonald, Ronald, 1998. "On the mean-reverting properties of target zone exchange rates: Some evidence from the ERM," European Economic Review, Elsevier, vol. 42(8), pages 1493-1523, September.
    9. Lars E. O. Svensson, 1992. "An Interpretation of Recent Research on Exchange Rate Target Zones," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 119-144, Fall.
    10. Ball, Clifford A. & Roma, Antonio, 1993. "A jump diffusion model for the European monetary system," Journal of International Money and Finance, Elsevier, vol. 12(5), pages 475-492, October.
    11. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
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