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Varying the VaR for Unconditional and Conditional Environments,

Cotter, John (2004): Varying the VaR for Unconditional and Conditional Environments,. Unpublished.

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Abstract

Accurate forecasting of risk is the key to successful risk management techniques. Using the largest stock index futures from twelve European bourses, this paper presents VaR measures based on their unconditional and conditional distributions for single and multi-period settings. These measures underpinned by extreme value theory are statistically robust explicitly allowing for fat-tailed densities. Conditional tail estimates are obtained by adjusting the unconditional extreme value procedure with GARCH filtered returns. The conditional modelling results in iid returns allowing for the use of a simple and efficient multi-period extreme value scaling law. The paper examines the properties of these distinct conditional and unconditional trading models. The paper finds that the biases inherent in unconditional single and multi-period estimates assuming normality extend to the conditional setting.

Item Type:MPRA Paper
Institution:University College Dublin
Language:English
Subjects:G - Financial Economics > G1 - General Financial Markets > G15 - International Financial Markets
G - Financial Economics > G1 - General Financial Markets > G10 - General
G - Financial Economics > G0 - General
ID Code:3483
Deposited By:John Cotter
Deposited On:12. Jun 2007
Last Modified:07. Nov 2007 03:13
References:

REFERENCES Andersen, T.G., T. Bollerslev, F.X. Diebold and Labys, P., 2000. Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian, Multinational Finance Journal, 4, 159-179. Artzner, P., DelBaen, F., Eber, J. and Heath, D., 1999. Coherent Measures of Risk, Mathematical Finance, 9, 203-228. Barone-Adesi, G., Giannopoulos, K. and Vosper, L., 1999. VaR without Correlations for Portfolios of Derivative Securities, Journal of Futures Markets, 19, 583-602. Cotter, J., 2001. Margin Exceedences for European Stock Index Futures using Extreme Value Theory, Journal of Banking and Finance, 25, 1475-1502. Dacorogna, M. M., Pictet, O. V, Muller, U.A, and de Vries, C. G., 1995. Extremal Forex Returns in Extremely Large Data Sets, Mimeo, Timbergen Institute. Danielsson, J. and de Vries, C. G., 2000. Value at Risk and Extreme Returns, Annales D’economie et de Statistque, 60, 239-270. de Haan, L., Resnick, S. I., Rootzen, H. R., and de Vries, C. G., 1989. Extremal Behaviour of Solutions to a Stochastic Difference Equation with Applications to ARCH processes, Stochastic Process and their Applications, 32: 213-224. Diebold, F. X., Schuermann, T. and Stroughair, J. D., 1998. Pitfalls and opportunities in the use of extreme value theory in risk management, in: J. D. Moody and A. N. Burgess (Eds.), Advances in Computational Finance, Kluwer, Amsterdam. Embrechts, P., Kluppelberg, C., and Mikosch, T., 1997. Modelling Extremal Events, Springer Verlag, Berlin. 21 Feller, W., 1972. An Introduction to Probability Theory and its Applications, John Wiley, New York. Ghose, D. and Kroner, K., 1995. The Relationship Between GARCH and Symmetric Stable Processes: Finding the Source of Fat Tails in Financial Data, Journal of Empirical Finance, 2, 225-251. Hill, B. M., 1975. A Simple General Approach to Inference about the Tail of a Distribution, Annals of Statistics, 3, 163-1174. Hull, J., and White, 1998. Incorporating Volatility Updating into the Historical Simulation Method for Value at Risk, Journal of Risk, 1, 5-19. Huisman, R., Koedijk, K. G., Kool, C. J. M., and Palm, F., 2001. Tail-Index Estimates in Small Samples, Journal of Business and Economic Statistics, 19, 208-216. Jansen, D. W., Koedijk, K. G. and and de Vries, C. G. 2000. Portfolio selection with limited downside risk, Journal of Empirical Finance, 7, 247-269. Kearns, P., and Pagan, A., 1997. Estimating the Density Tail Index for Financial Time Series, The Review of Economics and Statistics, 79, 171-175. Leadbetter, M. R., Lindgren G. and Rootzen, H., 1983. Extremes and Related Properties of Random Sequences and Processes, Springer Verlag, New York. Longin, F. M., 2000. From Value at Risk to Stress Testing, The Extreme Value Approach, Journal of Banking and Finance, 24, 127-152. Loretan, M. and Phillips, P. C. B., 1994. Testing the Covariance Stationarity of Heavy-tailed Time Series, Journal of Empirical Finance, 1, 211-248. McNeil, A. J., and Frey, R., 2000. Estimation of Tail-related Risk Measures for Heteroscedastic Financial Time Series: An Extreme Value Approach, Journal of Empirical Finance, 7, 271-300. Mikosch, T., and Starica, C., 2000. Limit Theory and Sample Autocorrelations and Extremes of a GARCH (1, 1) Process, Annals of Statistics, 28, 1427-1451. 22 Phillips, P. C. B., McFarland, J. W. and McMahon, P. C., 1996. Robust Tests of Forward Exchange Market Efficiency with Empirical Evidence from the 1920s, Journal of Applied Econometrics, 11, 1 - 22. Pownall, R. A., and Koedijk, K. G., 1999. Capturing downside risk in financial markets: the case of the Asian Crisis, Journal of International Money and Finance, 18, 853–870 Taylor, S. J., 1986, Modelling Financial Time Series, John Wiley, London.

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