Exchange Rate Returns Standardized by Realized Volatility Are (Nearly) Gaussian
The prescriptions of modern financial risk management hinge critically on the associated characterization of the distribution of future returns (cf., Diebold, Gunther and Tay, 1998, and Diebold, Hahn and Tay, 1999). Because volatility persistence renders high-frequency returns temporally dependent (e.g., Bollerslev, Chou and Kroner, 1992), it is the conditional return distribution, and not the unconditional distribution, that is of relevance for risk management. This is especially true in high-frequency situations, such as monitoring and managing the risk associated with the day-to-day operations of a trading desk, where volatility clustering is omnipresent. Exchange rate returns are well-known to be unconditionally symmetric but highly leptokurtic. Standardized daily or weekly returns from ARCH and related stochastic volatility models also appear symmetric but leptokurtic; that is, the distributions are not only unconditionally, but also conditionally leptokurtic, although less so than unconditionally.1 A sizable literature explicitly attempts to model the fat-tailed conditional distributions, including, for example, Bollerslev (1987), Engle and Gonzalez-Rivera (1991), and Hansen (1994).
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- Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999.
"The Distribution of Exchange Rate Volatility,"
New York University, Leonard N. Stern School Finance Department Working Paper Seires
99-059, New York University, Leonard N. Stern School of Business-.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," Center for Financial Institutions Working Papers 99-08, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Torben Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," NBER Working Papers 6961, National Bureau of Economic Research, Inc.
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- Drost, Feike C & Nijman, Theo E & Werker, Bas J M, 1998.
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American Statistical Association, vol. 16(2), pages 237-43, April.
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- Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
- Nelson, Daniel B., 1996. "A Note on the Normalized Errors in ARCH and Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 12(01), pages 113-128, March.
- Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
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"Aggregation and Model Construction for Volatility Models,"
141, Economics Group, Nuffield College, University of Oxford.
- Neil Shephard & Ole E. Barndorff-Nielsen, 1998. "Aggregation and model construction for volatility models," Economics Series Working Papers 1998-W07, University of Oxford, Department of Economics.
- Taylor, Stephen J. & Xu, Xinzhong, 1997. "The incremental volatility information in one million foreign exchange quotations," Journal of Empirical Finance, Elsevier, vol. 4(4), pages 317-340, December.
- Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
- 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.
- Francis X. Diebold & Jinyong Hahn & Anthony S. Tay, 1999. "Multivariate Density Forecast Evaluation And Calibration In Financial Risk Management: High-Frequency Returns On Foreign Exchange," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 661-673, November.
- Hansen, Bruce E, 1994.
"Autoregressive Conditional Density Estimation,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-30, August.
- Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
- Tom Doan, . "RATS programs to replicate Hansen's GARCH models with time-varying t-densities," Statistical Software Components RTZ00086, Boston College Department of Economics.
- Hsieh, David A, 1991. " Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-77, December.
- Hsieh, David A, 1989. "Modeling Heteroscedasticity in Daily Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 307-17, July.
- repec:cup:etheor:v:12:y:1996:i:1:p:113-28 is not listed on IDEAS
- Das, Sanjiv Ranjan & Sundaram, Rangarajan K., 1999.
"Of Smiles and Smirks: A Term Structure Perspective,"
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Cambridge University Press, vol. 34(02), pages 211-239, June.
- Sanjiv R. Das & Rangarajan K. Sundaram, 1998. "Of Smiles and Smirks: A Term-Structure Perspective," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-024, New York University, Leonard N. Stern School of Business-.
- Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
- Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
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