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Horizon Problems and Extreme Events in Financial Risk Management

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

Abstract

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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Bibliographic Info

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
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Handle: RePEc:wop:pennin:98-16

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  1. Francis X. Diebold & Jose A. Lopez, 1995. "Modeling volatility dynamics," Research Paper 9522, Federal Reserve Bank of New York.
  2. 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.
  3. Drost, F.C. & Nijman, T.E., 1990. "Temporal aggregation of GARCH processes," Discussion Paper 1990-66, Tilburg University, Center for Economic Research.
  4. Peter F. Christoffersen & Francis X. Diebold, 1998. "How Relevant is Volatility Forecasting for Financial Risk Management?," NBER Working Papers 6844, National Bureau of Economic Research, Inc.
  5. 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.
  6. Francis X. Diebold & Til Schuermann & John D. Stroughair, 1998. "Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management," Center for Financial Institutions Working Papers 98-10, Wharton School Center for Financial Institutions, University of Pennsylvania.
  7. Shorrocks, A F, 1978. "The Measurement of Mobility," Econometrica, Econometric Society, vol. 46(5), pages 1013-24, September.
  8. Koedijk, C.G. & Schafgans, M.M.A. & Vries, C.G. de, 1990. "The tail index of exchange rate returns," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3108722, Tilburg University.
  9. 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.
  10. 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.
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Cited by:
  1. Christoffersen, Peter & Errunza, Vihang, 2000. "Towards a global financial architecture: capital mobility and risk management issues," Emerging Markets Review, Elsevier, vol. 1(1), pages 3-20, May.
  2. Beverly J. Hirtle, 2003. "What market risk capital reporting tells us about bank risk," Economic Policy Review, Federal Reserve Bank of New York, issue Sep, pages 37-54.
  3. Bams, Dennis & Lehnert, Thorsten & Wolff, Christian C, 2002. "An Evaluation Framework for Alternative VaR Models," CEPR Discussion Papers 3403, C.E.P.R. Discussion Papers.
  4. Guidolin, Massimo & Timmermann, Allan, 2006. "Term structure of risk under alternative econometric specifications," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 285-308.
  5. Douglas D. Evanoff & Larry D. Wall, 2000. "Subordinated debt and bank capital reform," Working Paper Series WP-00-7, Federal Reserve Bank of Chicago.
  6. Gonzalez-Rivera, Gloria & Lee, Tae-Hwy & Mishra, Santosh, 2004. "Forecasting volatility: A reality check based on option pricing, utility function, value-at-risk, and predictive likelihood," International Journal of Forecasting, Elsevier, vol. 20(4), pages 629-645.
  7. Antonio Rubia & Trino-Manuel ��guez, 2006. "Forecasting the conditional covariance matrix of a portfolio under long-run temporal dependence," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(6), pages 439-458.
  8. Luca Erzegovesi, 2002. "VaR and Liquidity Risk.Impact on Market Behaviour and Measurement Issues," Alea Tech Reports 014, Department of Computer and Management Sciences, University of Trento, Italy, revised 14 Jun 2008.
  9. Flavio Bazzana, 2001. "I modelli interni per la valutazione del rischio di mercato secondo l'approccio del Value at Risk," Alea Tech Reports 011, Department of Computer and Management Sciences, University of Trento, Italy, revised 14 Jun 2008.
  10. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
  11. Gregory, Allan W. & Reeves, Jonathan J., 2008. "Interpreting Value at Risk (VaR) forecasts," Economic Systems, Elsevier, vol. 32(2), pages 167-176, June.
  12. Ho, Lan-Chih & Burridge, Peter & Cadle, John & Theobald, Michael, 2000. "Value-at-risk: Applying the extreme value approach to Asian markets in the recent financial turmoil," Pacific-Basin Finance Journal, Elsevier, vol. 8(2), pages 249-275, May.
  13. Andreas Lehnert & Wayne Passmore, 1999. "Pricing systemic crises: monetary and fiscal policy when savers are uncertain," Finance and Economics Discussion Series 1999-33, Board of Governors of the Federal Reserve System (U.S.).

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