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Horizon Problems and Extreme Events in Financial Risk Management

  • Peter F. Christoffersen
  • Francis X. Diebold
  • Til Schuermann

Central to the ongoing development of practical financial risk management methods is recognition of the fact that asset return volatility is often forecastable. Although there is no single horizon relevant for financial risk management, most would agree that in many situations the relevant horizon is quite long, certainly longer than a few days. This fact creates some tension, because although short-horizon asset return volatility is clearly highly forecastable, much less is known about long-horizon volatility forecastability, which we examine in this paper. We begin by assessing some common model-based methods for converting short-horizon volatility into long-horizon volatility; we argue that such conversions are problematic even when done properly. Hence we develop and apply a new model-free methodology to assess the forecastability of volatility across horizons and find, surprisingly, that forecastability decays rapidly as the horizon lengthens. We conclude that for managing risk at horizons longer than a few weeks, attention given to direct estimation of extreme event probabilities may be more productive than attention given to modeling volatility dynamics, and we proceed to assess the potential of extreme value theory for estimating extreme event probabilities.

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Paper provided by Wharton School Center for Financial Institutions, University of Pennsylvania in its series Center for Financial Institutions Working Papers with number 98-16.

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Date of creation: Apr 1998
Date of revision:
Handle: RePEc:wop:pennin:98-16
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  1. Francis X. Diebold & Til Schuermann & John D. Stroughair, 1998. "Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-081, New York University, Leonard N. Stern School of Business-.
  2. Francis X. Diebold & Andrew Hickman & Atsushi Inoue & Til Schuermann, 1997. "Converting 1-Day Volatility to h-Day Volatitlity: Scaling by Root-h is Worse Than You Think," Center for Financial Institutions Working Papers 97-34, Wharton School Center for Financial Institutions, University of Pennsylvania.
  3. Drost, F.C. & Nijman, T.E., 1990. "Temporal Aggregation Of Garch Processes," Papers 9066, Tilburg - Center for Economic Research.
  4. Shorrocks, A F, 1978. "The Measurement of Mobility," Econometrica, Econometric Society, vol. 46(5), pages 1013-24, September.
  5. 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.
  6. Peter F. Christoffersen & Francis X. Diebold, 1998. "How Relevant is Volatility Forecasting for Financial Risk Management?," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-080, New York University, Leonard N. Stern School of Business-.
  7. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
  8. Francis X. Diebold & Jose A. Lopez, 1995. "Modeling volatility dynamics," Research Paper 9522, Federal Reserve Bank of New York.
  9. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  10. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier.
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