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A Note on Estimating Realignment Probabilities -- A First-Passage-Time Approach

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  • Cho-Hoi Hui

    (Research Department, Hong Kong Monetary Authority)

  • Chi-Fai Lo

    (Research Department, Hong Kong Monetary Authority)

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    Abstract

    This paper proposes a path-dependent approach for estimating realignment probabilities of targeted exchange rates based on first-passage-time distributions instead of the commonly used path-independent approach. We consider that path dependency is an intrinsic characteristic of realignment risk because a realignment of an exchange rate can occur whenever a committed band by a central bank is breached. A mean-reverting lognormal process is considered in the first-passage-time approach. Based on market data of the British pound and mark during the ERM crisis of 1992, the realignment probabilities of the pound estimated under the proposed approach show that path dependency is quantitatively significant, compared with the path-independent approach.

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    File URL: http://www.info.gov.hk/hkma/eng/research/working/pdf/HKMAWP08_09_full.pdf
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    Bibliographic Info

    Paper provided by Hong Kong Monetary Authority in its series Working Papers with number 0809.

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    Length: 15 pages
    Date of creation: Jun 2008
    Date of revision:
    Handle: RePEc:hkg:wpaper:0809

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    Related research

    Keywords: realignment risk; mean-reversion; first-passage-time probability;

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    References

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    1. Clifford Ball & Antonio Roma, 1998. "Detecting mean reversion within reflecting barriers: application to the European Exchange Rate Mechanism," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(1), pages 1-15.
    2. 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.
    3. Campa, J.M. & Chang, P.H.K., 1995. "Arbitrage-Based Tests of Target Zone Credibility: Evidence from ERM Cross-Rate Options," Papers 95-25, Columbia - Graduate School of Business.
    4. Krugman, Paul R, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, MIT Press, vol. 106(3), pages 669-82, August.
    5. Ball, Clifford A. & Torous, Walter N., 1983. "A Simplified Jump Process for Common Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(01), pages 53-65, March.
    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. 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.
    8. Ball, Clifford A & Torous, Walter N, 1985. " On Jumps in Common Stock Prices and Their Impact on Call Option Pricing," Journal of Finance, American Finance Association, vol. 40(1), pages 155-73, March.
    9. Bates, David S., 1996. "Dollar jump fears, 1984-1992: distributional abnormalities implicit in currency futures options," Journal of International Money and Finance, Elsevier, vol. 15(1), pages 65-93, February.
    10. 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.
    11. 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.
    12. Fred G M C Nieuwland & Willem F C Verschoor & Christian C P Wolff, 1990. "EMS Exchange Rates," CEPR Financial Markets Paper 0002, European Science Foundation Network in Financial Markets, c/o C.E.P.R, 77 Bastwick Street, London EC1V 3PZ.
    13. 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.
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    Cited by:
    1. Hans Genberg & Cho-hoi Hui, 2009. "The Credibility of the Link from the Perspective of Modern Financial Theory," Working Papers 0902, Hong Kong Monetary Authority.

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