IDEAS home Printed from https://ideas.repec.org/a/ijf/ijfiec/v13y2008i1p118-134.html
   My bibliography  Save this article

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

Author

Listed:
  • 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)

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.

Suggested Citation

  • C. H. Hui & C. F. Lo & V. Yeung & L. Fung, 2008. "Valuing foreign currency options with a mean-reverting process: a study of Hong Kong dollar," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 13(1), pages 118-134.
    • Handle: RePEc:ijf:ijfiec:v:13:y:2008:i:1:p:118-134
    DOI: 10.1002/ijfe.346
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1002/ijfe.346
    File Function: Link to full text; subscription required
    Download Restriction: no
    File URL: https://libkey.io/10.1002/ijfe.346?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
    ---><---

    References listed on IDEAS

    as
    1. Soderlind, Paul & Svensson, Lars, 1997. "New techniques to extract market expectations from financial instruments," Journal of Monetary Economics, Elsevier, vol. 40(2), pages 383-429, October.
    2. 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.
    3. Nieuwland, Frederick G M C & Verschoor, Willem F C & Wolff, Christian C P, 1994. "Stochastic trends and jumps in EMS exchange rates," Journal of International Money and Finance, Elsevier, vol. 13(6), pages 699-727, December.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(3), pages 669-682.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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 637-654, May-June.
    12. 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.
    13. Svensson, Lars E. O., 1993. "Assessing target zone credibility : Mean reversion and devaluation expectations in the ERM, 1979-1992," European Economic Review, Elsevier, vol. 37(4), pages 763-793, May.
    14. 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.
    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. Hui, Cho-Hoi & Lo, Chi-Fai & Liu, Chi-Hei, 2022. "Exchange rate dynamics with crash risk and interventions," International Review of Economics & Finance, Elsevier, vol. 79(C), pages 18-37.
    2. Peter Carr, 2017. "Bounded Brownian Motion," Risks, MDPI, vol. 5(4), pages 1-11, November.

    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. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    2. Hui, C.H. & Lo, C.F., 2009. "A note on estimating realignment probabilities - A first-passage-time approach," Journal of International Money and Finance, Elsevier, vol. 28(5), pages 804-812, September.
    3. Cho-Hoi Hui & Chi-Fai Lo & Po-Hon Chau, 2017. "Can Exchange Rate Dynamics in Krugman¡¯s Target-zone Model be Directly Tested?Abstract: Despite Krugman's (1991) model being a benchmark for modelling target zones, empirical support has been sparse d," Working Papers 032017, Hong Kong Institute for Monetary Research.
    4. Lo, C.F. & Hui, C.H. & Fong, T. & Chu, S.W., 2015. "A quasi-bounded target zone model — Theory and application to Hong Kong dollar," International Review of Economics & Finance, Elsevier, vol. 37(C), pages 1-17.
    5. Hui, Cho-Hoi & Lo, Chi-Fai & Fong, Tom Pak-Wing, 2016. "Swiss franc's one-sided target zone during 2011–2015," International Review of Economics & Finance, Elsevier, vol. 44(C), pages 54-67.
    6. Peter P. Carr & Zura Kakushadze, 2017. "FX options in target zones," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1477-1486, October.
    7. António Portugal Duarte & João Sousa Andrade & Adelaide Duarte, 2009. "Exchange Rate Mean Reversion within a Target Zone: Evidence from a Country on the Periphery of the ERM," GEMF Working Papers 2009-15, GEMF, Faculty of Economics, University of Coimbra.
    8. Genberg, Hans & Hui, Cho-Hoi, 2008. "The credibility of 'The Link' from the perspective of modern financial theory," IMFS Working Paper Series 18, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    9. Cho-Hoi Hui & Chi-Fai Lo, 2008. "A Note on Estimating Realignment Probabilities -- A First-Passage-Time Approach," Working Papers 0809, Hong Kong Monetary Authority.
    10. Malz, Allan M., 1996. "Using option prices to estimate realignment probabilities in the European Monetary System: the case of sterling-mark," Journal of International Money and Finance, Elsevier, vol. 15(5), pages 717-748, October.
    11. Marie Bessec, 2000. "Mean-Reversion versus PPP Adjustment: The Two Regimes of Exchange Rate Dynamics Under the EMS, 1979-1998," Econometric Society World Congress 2000 Contributed Papers 1305, Econometric Society.
    12. Bekaert, Geert & Gray, Stephen F., 1998. "Target zones and exchange rates:: An empirical investigation," Journal of International Economics, Elsevier, vol. 45(1), pages 1-35, June.
    13. 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.
    14. Pierdzioch, Christian, 2000. "The Effectiveness of the FX Market Interventions of the Bundesbank During the Louvre Period: An Options-Based Analysis," Kiel Working Papers 971, Kiel Institute for the World Economy (IfW Kiel).
    15. 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.
    16. Alexandra Janssen & Rahel Studer, 2014. "The Swiss franc's honeymoon," ECON - Working Papers 170, Department of Economics - University of Zurich, revised Jan 2017.
    17. Jose Manuel Campa & P.H. Kevin Chang, 1996. "Options-based evidence of the credibility of the peseta in the ERM," Investigaciones Economicas, Fundación SEPI, vol. 20(1), pages 3-22, January.
    18. C. H. Hui & C. F. Lo & T. Fong, 2015. "A Quasi-Bounded Model for Swiss Franc's One-Sided Target Zone During 2011-2015," Working Papers 152015, Hong Kong Institute for Monetary Research.
    19. Gabauer, David, 2021. "Dynamic measures of asymmetric & pairwise connectedness within an optimal currency area: Evidence from the ERM I system," Journal of Multinational Financial Management, Elsevier, vol. 60(C).
    20. Darvas, Zsolt, 1999. "Az árfolyamsávok empirikus modelljei és a devizaárfolyam sávon belüli előrejelezhetetlensége [Empirical models of exchange rate target zones]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(6), pages 507-529.

    More about this item

    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:ijf:ijfiec:v:13:y:2008:i:1:p:118-134. 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: Wiley-Blackwell Digital Licensing or Christopher F. Baum (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/1076-9307/ .

    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.