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Asymmetric power distribution: Theory and applications to risk measurement

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Author Info
Ivana Komunjer (Department of Economics, University of California, San Diego, California, USA)

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Abstract

Theoretical 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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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 22 (2007)
Issue (Month): 5 ()
Pages: 891-921
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Handle: RePEc:jae:japmet:v:22:y:2007:i:5:p:891-921

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September. [Downloadable!] (restricted)
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  2. Olivier SCAILLET, 2004. "Nonparametric Estimation of Conditional Expected Shortfall," FAME Research Paper Series rp112, International Center for Financial Asset Management and Engineering. [Downloadable!]
  3. Feldstein, Martin S, 1969. "Mean-Variance Analysis in the Theory of Liquidity Preference and Portfolio Selection," Review of Economic Studies, Blackwell Publishing, vol. 36(105), pages 5-12, January. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
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  5. Andrews, Donald W.K., 1986. "Empirical process methods in econometrics," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 37, pages 2247-2294 Elsevier. [Downloadable!] (restricted)
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  6. Hanoch, G & Levy, Haim, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Blackwell Publishing, vol. 36(107), pages 335-46, July. [Downloadable!] (restricted)
  7. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
  8. Kjersti Aas & Ingrid Hobaek Haff, 2006. "The Generalized Hyperbolic Skew Student's t-Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 275-309. [Downloadable!] (restricted)
  9. Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 53-89. [Downloadable!] (restricted)
  10. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447. [Downloadable!] (restricted)
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  1. Mohammed Bouaddi & Jeroen V.K. Rombouts, 2007. "Mixed Exponential Power Asymmetric Conditional Heteroskedasticity," Cahiers de recherche 0749, CIRPEE. [Downloadable!]
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