Asymmetric power distribution: Theory and applications to risk measurement
AbstractTheoretical literature in finance has shown that the risk of financial time series can be well quantified by their expected shortfall, also known as the tail value-at-risk. In this paper, I construct a parametric estimator for the expected shortfall based on a flexible family of densities, called the asymmetric power distribution (APD). The APD family extends the generalized power distribution to cases where the data exhibits asymmetry. The first contribution of the paper is to provide a detailed description of the properties of an APD random variable, such as its quantiles and expected shortfall. The second contribution of the paper is to derive the asymptotic distribution of the APD maximum likelihood estimator (MLE) and construct a consistent estimator for its asymptotic covariance matrix. The latter is based on the APD score whose analytic expression is also provided. A small Monte Carlo experiment examines the small sample properties of the MLE and the empirical coverage of its confidence intervals. An empirical application to four daily financial market series reveals that returns tend to be asymmetric, with innovations which cannot be modeled by either Laplace (double-exponential) or Gaussian distribution, even if we allow the latter to be asymmetric. In an out-of-sample exercise, I compare the performances of the expected shortfall forecasts based on the APD-GARCH, Skew-t-GARCH and GPD-EGARCH models. While the GPD-EGARCH 1% expected shortfall forecasts seem to outperform the competitors, all three models perform equally well at forecasting the 5% and 10% expected shortfall. Copyright © 2007 John Wiley & Sons, Ltd.
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Bibliographic InfoArticle provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.
Volume (Year): 22 (2007)
Issue (Month): 5 ()
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Other versions of this item:
- Ivana Komunjer, 2004. "Asymmetric Power Distribution: Theory and Applications to Risk Measurement," Econometric Society 2004 Latin American Meetings 44, Econometric Society.
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
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- Feldstein, Martin S, 1969. "Mean-Variance Analysis in the Theory of Liquidity Preference and Portfolio Selection," Review of Economic Studies, Wiley Blackwell, vol. 36(105), pages 5-12, January.
- Fitzenberger, Bernd, 1998. "The moving blocks bootstrap and robust inference for linear least squares and quantile regressions," Journal of Econometrics, Elsevier, vol. 82(2), pages 235-287, February.
- Komunjer, Ivana, 2002.
"Quasi-Maximum Likelihood Estimation for Conditional Quantiles,"
1139, California Institute of Technology, Division of the Humanities and Social Sciences.
- Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September.
- Hanoch, G & Levy, Haim, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Wiley Blackwell, vol. 36(107), pages 335-46, July.
- Donald W.K. Andrews, 1993.
"Empirical Process Methods in Econometrics,"
Cowles Foundation Discussion Papers
1059, Cowles Foundation for Research in Economics, Yale University.
- Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 53-89.
- Giot,Pierre & Laurent,Sebastien, 2001.
"Modelling daily value-at-risk using realized volatility and arch type models,"
014, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
- Giot, Pierre & Laurent, Sebastien, 2004. "Modelling daily Value-at-Risk using realized volatility and ARCH type models," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 379-398, June.
- Pierre Giot & Sébastien Laurent, 2002. "Modelling Daily Value-at-Risk Using Realized Volatility and ARCH Type Models," Computing in Economics and Finance 2002 52, Society for Computational Economics.
- GIOT, Pierre & LAURENT, Sébastien, . "Modelling daily Value-at-Risk using realized volatility and ARCH type models," CORE Discussion Papers RP -1708, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Olivier SCAILLET, 2004. "Nonparametric Estimation of Conditional Expected Shortfall," FAME Research Paper Series rp112, International Center for Financial Asset Management and Engineering.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Kjersti Aas & Ingrid Hobaek Haff, 2006. "The Generalized Hyperbolic Skew Student's t-Distribution," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(2), pages 275-309.
- Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
- Mendoza-Velázquez, Alfonso & Galvanovskis, Evalds, 2009. "Introducing the GED-Copula with an application to Financial Contagion in Latin America," MPRA Paper 46669, University Library of Munich, Germany, revised 01 Feb 2010.
- Zhu, Dongming & Zinde-Walsh, Victoria, 2009.
"Properties and estimation of asymmetric exponential power distribution,"
Journal of Econometrics,
Elsevier, vol. 148(1), pages 86-99, January.
- ZHU, Dongming & ZINDE-WALSH, Victoria, 2007. "Properties and Estimation of Asymmetric Exponential Power Distribution," Cahiers de recherche 13-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Victoria Zinde-Walsh & Dongming Zhu, 2007. "Properties And Estimation Of Asymmetric Exponential Power Distribution," Departmental Working Papers 2007-11, McGill University, Department of Economics.
- Li, Xiao-Ming & Rose, Lawrence C., 2009. "The tail risk of emerging stock markets," Emerging Markets Review, Elsevier, vol. 10(4), pages 242-256, December.
- Zhu, Dongming & Galbraith, John W., 2011. "Modeling and forecasting expected shortfall with the generalized asymmetric Student-t and asymmetric exponential power distributions," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 765-778, September.
- BOUADDI, Mohammed & ROMBOUTS, Jeroen V.K., 2007.
"Mixed exponential power asymmetric conditional heteroskedasticity,"
CORE Discussion Papers
2007097, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Rombouts Jeroen V. K. & Bouaddi Mohammed, 2009. "Mixed Exponential Power Asymmetric Conditional Heteroskedasticity," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(3), pages 1-32, May.
- Mohammed Bouaddi & Jeroen V.K. Rombouts, 2007. "Mixed Exponential Power Asymmetric Conditional Heteroskedasticity," Cahiers de recherche 0749, CIRPEE.
- Mohammed Bouaddi & Jeroen V.K. Rombouts, 2007. "Mixed Exponential Power Asymmetric Conditional Heteroskedasticity," Cahiers de recherche 07-15, HEC Montréal, Institut d'économie appliquée.
- Komunjer, Ivana & Vuong, Quang, 2010. "Efficient estimation in dynamic conditional quantile models," Journal of Econometrics, Elsevier, vol. 157(2), pages 272-285, August.
- Fischer, Matthias, 2012. "A skew and leptokurtic distribution with polynomial tails and characterizing functions in closed form," IWQW Discussion Paper Series 03/2012, Friedrich-Alexander-Universität Erlangen-Nürnberg, Institut für Wirtschaftspolitik und Quantitative Wirtschaftsforschung (IWQW).
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