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Empirical modeling of the DEM/USD and DEM/JPY foreign exchange rate: Structural shifts in GARCH-models and their implications

  • Herwartz, Helmut
  • Reimers, Hans-Eggert

We analyze daily changes of two log foreign exchange (FX) rates involving the Deutsche Mark (DEM) for the period 1975 - 1998, namely FX-rates measured against the US dollar (USD) and the Japanese yen (JPY). Ta account for volatility e1ustering we fit a GARCH(l,l)-model with leptokurtic innovations. Its parameters are not stable over the sample period and two separate variance regimes are selected for both exchange rate series. The identified points of structural change are close to a change of the monetary policies in the US and Japan, the latter of which is followed by a long period of decreasing asset prices. Having identified subperiods of homogeneous volatility dynamics we concentrate on stylized facts to distinguish these volatility regimes. The bottom level of estimated volatility turns out be considerably higher during the second part of the sample period for both exchange rates. A similar result holds for the average level of volatility and for implied volatility of heavily traded at the money options.

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Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 2001,83.

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Date of creation: 2001
Date of revision:
Handle: RePEc:zbw:sfb373:200183
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  1. Takatoshi Ito & Tokuo Iwaisako, 1995. "Explaining Asset Bubbles in Japan," NBER Working Papers 5358, National Bureau of Economic Research, Inc.
  2. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
  3. Hafner, Christian M. & Herwartz, Helmut, 2001. "Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis," Journal of Empirical Finance, Elsevier, vol. 8(1), pages 1-34, March.
  4. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
  5. Harris, Lawrence, 1989. " S&P 500 Cash Stock Price Volatilities," Journal of Finance, American Finance Association, vol. 44(5), pages 1155-75, December.
  6. 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.
  7. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  8. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-96, May.
  9. Lastrapes, William D, 1989. "Exchange Rate Volatility and U.S. Monetary Policy: An ARCH Application," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 21(1), pages 66-77, February.
  10. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
  11. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Persistence in Variance, Structural Change, and the GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 225-34, April.
  12. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
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