Value-at-risk for long and short trading positions
In this paper we model Value-at-Risk (VaR) for daily asset returns using a collection of parametric univariate and multivariate models of the ARCH class based on the skewed Student distribution. We show that models that rely on a symmetric density distribution for the error term underperform with respect to skewed density models when the left and right tails of the distribution of returns must be modelled. Thus, VaR for traders having both long and short positions is not adequately modelled using usual normal or Student distributions. We suggest using an APARCH model based on the skewed Student distribution (combined with a time-varying correlation in the multivariate case) to fully take into account the fat left and right tails of the returns distribution. This allows for an adequate modelling of large returns defined on long and short trading positions. The performances of the univariate models are assessed on daily data for three international stock indexes and three US stocks of the Dow Jones index. In a second application, we consider a portfolio of three US stocks and model its long and short VaR using a multivariate skewed Student density. Copyright © 2003 John Wiley & Sons, Ltd.
Volume (Year): 18 (2003)
Issue (Month): 6 ()
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- Darryll Hendricks, 1996. "Evaluation of value-at-risk models using historical data," Economic Policy Review, Federal Reserve Bank of New York, issue Apr, pages 39-69.
- Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
- Peter F. Christoffersen & Francis X. Diebold, 2000.
"How Relevant is Volatility Forecasting for Financial Risk Management?,"
The Review of Economics and Statistics,
MIT Press, vol. 82(1), pages 12-22, February.
- Peter F. Christoffersen & Francis X. Diebold, 1997. "How Relevant is Volatility Forecasting for Financial Risk Management?," Center for Financial Institutions Working Papers 97-45, Wharton School Center for Financial Institutions, University of Pennsylvania.
- 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-.
- 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.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
- Schwert, G William, 1990.
"Stock Volatility and the Crash of '87,"
Review of Financial Studies,
Society for Financial Studies, vol. 3(1), pages 77-102.
- Chris Brooks & Gita Persand, 2000. "Value at Risk and Market Crashes," ICMA Centre Discussion Papers in Finance icma-dp2000-01, Henley Business School, Reading University.
- Billio, Monica & Pelizzon, Loriana, 2000. "Value-at-Risk: a multivariate switching regime approach," Journal of Empirical Finance, Elsevier, vol. 7(5), pages 531-554, December.
- BAUWENS, Luc & LAURENT, Sébastien, 2002.
"A new class of multivariate skew densities, with application to GARCH models,"
CORE Discussion Papers
2002020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Luc Bauwens & Sébastien Laurent, 2002. "A New Class of Multivariate skew Densities, with Application to GARCH Models," Computing in Economics and Finance 2002 5, Society for Computational Economics.
- He, Changli & Teräsvirta, Timo, 1999. "Higher-order dependence in the general Power ARCH process and a special case," SSE/EFI Working Paper Series in Economics and Finance 315, Stockholm School of Economics.
- R. F. Engle & A. J. Patton, 2001. "What good is a volatility model?," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 237-245.
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, .
"Multivariate GARCH models: a survey,"
CORE Discussion Papers RP
1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
- Pagan, Adrian R. & Schwert, G. William, 1990.
"Alternative models for conditional stock volatility,"
Journal of Econometrics,
Elsevier, vol. 45(1-2), pages 267-290.
- Adrian R. Pagan & G. William Schwert, 1989. "Alternative Models For Conditional Stock Volatility," NBER Working Papers 2955, National Bureau of Economic Research, Inc.
- Pagan, A.R. & Schwert, G.W., 1989. "Alternative Models For Conditional Stock Volatility," Papers 89-02, Rochester, Business - General.
- Laurent, Sebastien & Peters, Jean-Philippe, 2002. " G@RCH 2.2: An Ox Package for Estimating and Forecasting Various ARCH Models," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 447-85, July.
- Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
- O. Scaillet, 2004. "Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 115-129.
- Ng, Victor & Engle, Robert F. & Rothschild, Michael, 1992. "A multi-dynamic-factor model for stock returns," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 245-266.
- French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
- Xu, Xinzhong & Taylor, Stephen J., 1995. "Conditional volatility and the informational efficiency of the PHLX currency options market," Journal of Banking & Finance, Elsevier, vol. 19(5), pages 803-821, August.
- Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December.
- M, El Babsiri & Jean-Michel Zakoïan, 1997.
"Contemporaneous Asymmetry in GARCH Processes,"
97-03, Centre de Recherche en Economie et Statistique.
- Hansen, B.E., 1992.
"Autoregressive Conditional Density Estimation,"
RCER Working Papers
322, University of Rochester - Center for Economic Research (RCER).
- Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
- GIOT, Pierre, 2002. "The information content of implied volatility in agricultural commodity markets," CORE Discussion Papers 2002038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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