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Continuous time regime switching model applied to foreign exchange rate

Author

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  • Stéphane Goutte

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Benteng Zou

    (Center for Research in Economic Analysis CREA - CREA - Center for Research in Economic Analysis - uni.lu - Université du Luxembourg = University of Luxembourg = Universität Luxemburg)

Abstract

Modified Cox-Ingersoll-Ross model is employed, combining with Hamilton (1989) type Markov regime switching framework, to study foreign exchange rates, where all parameter values depend on the value of a continuous time Markov chain. Basing on real data of some foreign exchange rates, the Expectation-Maximization algorithm is extended to this more general model and it is applied to calibrate all parameters. We compare the obtained results regarding to results obtained with non regime switching models and notice that our results match much better the reality than the others without Markov switching. Furthermore, we illustrate our model on various foreign exchange rate data and clarify some significant eco- nomic time periods in which financial or economic crisis appeared, thus, regime switching obtained.

Suggested Citation

  • Stéphane Goutte & Benteng Zou, 2012. "Continuous time regime switching model applied to foreign exchange rate," Working Papers hal-00643900, HAL.
    • Handle: RePEc:hal:wpaper:hal-00643900
    Note: View the original document on HAL open archive server: https://hal.science/hal-00643900v2
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    References listed on IDEAS

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    1. Rossi, Barbara, 2005. "Optimal Tests For Nested Model Selection With Underlying Parameter Instability," Econometric Theory, Cambridge University Press, vol. 21(5), pages 962-990, October.
    2. Hélène Baron & Guillaume Baron, 2002. "Un indicateur probabiliste de retournement conjoncturel dans la zone euro," Économie et Statistique, Programme National Persée, vol. 359(1), pages 101-121.
    3. Fernando Alvarez & Andrew Atkeson & Patrick J. Kehoe, 2008. "If exchange rates are random walks, then almost everything we say about monetary policy is wrong," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Jul, pages 2-9.
    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    5. Calvet, Laurent E. & Fisher, Adlai J., 2008. "Multifractal Volatility," Elsevier Monographs, Elsevier, edition 1, number 9780121500139.
    6. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    7. Caporale, Guglielmo Maria & Pittis, Nikitas, 1995. "Nominal exchange rate regimes and the stochastic behavior of real variables," Journal of International Money and Finance, Elsevier, vol. 14(3), pages 395-415, June.
    8. Engel, Charles & Hamilton, James D, 1990. "Long Swings in the Dollar: Are They in the Data and Do Markets Know It?," American Economic Review, American Economic Association, vol. 80(4), pages 689-713, September.
    9. Ang, Andrew & Bekaert, Geert, 2002. "Regime Switches in Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 163-182, April.
    10. Cheung, Yin-Wong & Erlandsson, Ulf G., 2005. "Exchange Rates and Markov Switching Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 314-320, July.
    11. Cheung, Yin-Wong & Chinn, Menzie D. & Pascual, Antonio Garcia, 2005. "Empirical exchange rate models of the nineties: Are any fit to survive?," Journal of International Money and Finance, Elsevier, vol. 24(7), pages 1150-1175, November.
    12. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    13. Baele, Lieven, 2005. "Volatility Spillover Effects in European Equity Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 40(2), pages 373-401, June.
    14. Jose A. Lopez, 1996. "Exchange rate cointegration across central bank regime shifts," Research Paper 9602, Federal Reserve Bank of New York.
    15. Engel, Charles & Hakkio, Craig S, 1996. "The Distribution of Exchange Rates in the EMS," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 1(1), pages 55-67, January.
    16. Bergman, U. Michael & Hansson, Jesper, 2005. "Real exchange rates and switching regimes," Journal of International Money and Finance, Elsevier, vol. 24(1), pages 121-138, February.
    17. Joanna Janczura & Rafał Weron, 2012. "Efficient estimation of Markov regime-switching models: An application to electricity spot prices," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(3), pages 385-407, July.
    18. Choi Seungmoon, 2009. "Regime-Switching Univariate Diffusion Models of the Short-Term Interest Rate," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(1), pages 1-41, March.
    19. 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..
    20. Laurent E. Calvet & Adlai Fisher, 2008. "Multifractal Volatility: Theory, Forecasting and Pricing," Post-Print hal-00671877, HAL.
    21. Rossi, Barbara, 2006. "Are Exchange Rates Really Random Walks? Some Evidence Robust To Parameter Instability," Macroeconomic Dynamics, Cambridge University Press, vol. 10(1), pages 20-38, February.
    22. Hansen, Bruce E, 1992. "The Likelihood Ratio Test under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 61-82, Suppl. De.
    23. Margaret M. McConnell & Gabriel Perez-Quiros, 2000. "Output fluctuations in the United States: what has changed since the early 1980s?," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    24. Bollen, Nicolas P. B. & Gray, Stephen F. & Whaley, Robert E., 2000. "Regime switching in foreign exchange rates: Evidence from currency option prices," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 239-276.
    25. Kaushik I. Amin & Robert A. Jarrow, 2008. "Pricing foreign currency options under stochastic interest rates," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 14, pages 307-326, World Scientific Publishing Co. Pte. Ltd..
    26. Jushan Bai & Peng Wang, 2011. "Conditional Markov chain and its application in economic time series analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(5), pages 715-734, August.
    27. Naszodi, Anna, 2011. "Exchange rate dynamics under state-contingent stochastic process switching," Journal of International Money and Finance, Elsevier, vol. 30(5), pages 896-908, September.
    28. Qiang Fu, 1996. "On the valuation of an option to exchange one interest rate for another," Journal of Banking & Finance, Elsevier, vol. 20(4), pages 645-653, May.
    29. Ferrara, L., 2008. "The contribution of cyclical turning point indicators to business cycle analysis," Quarterly selection of articles - Bulletin de la Banque de France, Banque de France, issue 13, pages 49-61, Autumn.
    30. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
    31. Kontolemis, Zenon G, 2001. "Analysis of the US Business Cycle with a Vector-Markov-Switching Model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(1), pages 47-61, January.
    32. Monica Billio & Roberto Casarin, 2010. "Bayesian Estimation of Stochastic-Transition Markov-Switching Models for Business Cycle Analysis," Working Papers 1002, University of Brescia, Department of Economics.
    33. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
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    Cited by:

    1. Raphaël Homayoun Boroumand & Stéphane Goutte & Simon Porcher & Thomas Porcher, 2014. "A Conditional Markov Regime Switching Model to Study Margins: Application to the French Fuel Retail Markets," Working Papers hal-01090837, HAL.
    2. Olivier Damette & Stéphane Goutte, 2014. "Tobin tax and trading volume tightening: a reassessment," Working Papers halshs-00926805, HAL.
    3. Julien Chevallier & Stéphane Goutte & Khaled Guesmi & Samir Saadi, 2019. "Study of the dynamic of Bitcoin's price," Working Papers halshs-02175669, HAL.
    4. Julien Chevallier & St�phane Goutte, 2015. "Detecting jumps and regime switches in international stock markets returns," Applied Economics Letters, Taylor & Francis Journals, vol. 22(13), pages 1011-1019, September.
    5. Boroumand, Raphaël Homayoun & Goutte, Stéphane & Porcher, Simon & Porcher, Thomas, 2016. "Asymmetric evidence of gasoline price responses in France: A Markov-switching approach," Economic Modelling, Elsevier, vol. 52(PB), pages 467-476.
    6. Goutte, Stéphane, 2014. "Conditional Markov regime switching model applied to economic modelling," Economic Modelling, Elsevier, vol. 38(C), pages 258-269.
    7. Julien Chevallier & Stéphane Goutte & Khaled Guesmi & Samir Saadi, 2019. "On the Bitcoin price dynamics: an augmented Markov-Switching model with Lévy jumps," Working Papers halshs-02120636, HAL.
    8. Stéphane Goutte & Amine Ismail & Huyên Pham, 2017. "Regime-switching Stochastic Volatility Model : Estimation and Calibration to VIX options," Working Papers hal-01212018, HAL.

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    Keywords

    Foreign exchange rate; Regime switching model; calibration; financial crisis;
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