Valuing foreign currency options with a mean-reverting process: a study of Hong Kong dollar
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.
Volume (Year): 13 (2008)
Issue (Month): 1 ()
|Contact details of provider:|| Web page: http://www.interscience.wiley.com/jpages/1076-9307/|
|Order Information:||Web: http://jws-edcv.wiley.com/jcatalog/JournalsCatalogOrder/JournalOrder?PRINT_ISSN=1076-9307|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Söderlind, Paul & Svensson, Lars E.O., 1996. "New Techniques to Extract Market expectations from Financial Instruments," SSE/EFI Working Paper Series in Economics and Finance 142, Stockholm School of Economics.
- Söderlind, Paul & Svensson, Lars E O, 1997. "New Techniques to Extract Market Expectations from Financial Instruments," CEPR Discussion Papers 1556, C.E.P.R. Discussion Papers.
- Soderlind, P & Svensson, L-E-O, 1996. "New Techniques to Extract Market Expectations from Financial Instruments," Papers 621, Stockholm - International Economic Studies.
- 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.
- Söderlind, Paul & Svensson, Lars E.O., 1997. "New Techniques to Extract Market Expectations from Financial Instruments," Seminar Papers 621, Stockholm University, Institute for International Economic Studies.
- 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.
- Andrew K. Rose & Lars E.O. Svensson, 1993. "European Exchange Rate Credibility Before the Fall," NBER Working Papers 4495, National Bureau of Economic Research, Inc.
- Rose, A.K. & Svensson, L.E.O., 1993. "European Exchange Rate Credibility Before the Fall," Papers 542, Stockholm - International Economic Studies.
- Rose, Andrew K & Svensson, Lars E O, 1993. "European Exchange Rate Credibility Before the Fall," CEPR Discussion Papers 852, C.E.P.R. Discussion Papers.
- Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
- Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
- 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.
- Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, Oxford University Press, vol. 106(3), pages 669-682.
- 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.
- 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.
- Lars E.O. Svensson, 1991. "Assessing Target Zone Credibility: Mean Reversion and Devaluation Expectations in the ERM 1979-1992," NBER Working Papers 3795, National Bureau of Economic Research, Inc.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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. Full references (including those not matched with items on IDEAS)
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.
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)
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.