Asymmetric Power Distribution: Theory and Applications to Risk Measurement
Theoretical literature in finance has shown that quantifying the risk of financial time series amounts to measuring their expected shortfall, also known as tail Value at Risk. Unfortunately, little empirical work has been devoted to the problem of modeling and inference of such risk measures and, in particular, to their estimation. In this paper, we construct a parametric estimator for the expected shortfall based on a new family of densities, which we call the Asymmetric Power Distribution (APD). The APD family extends the Generalized Power Distribution to cases where the data exhibits asymmetry. We provide a detailed description of the properties of an APD random variable, such as its quantiles, moments and moment related parameters. Moreover, we discuss the problem of simulation of such random variables and provide maximum likelihood estimates of the APD density parameters. The study of asymptotic properties of the latter falls outside the standard framework due to the non-differentiability of the APD log-likelihood. An empirical application to six 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. Under a more general assumption that the return innovations are APD, we are able to compute expected shortfalls and corresponding confidence intervals and thus compare the riskiness of the series examined
|Date of creation:||11 Aug 2004|
|Date of revision:|
|Contact details of provider:|| Phone: 1 212 998 3820|
Fax: 1 212 995 4487
Web page: http://www.econometricsociety.org/pastmeetings.asp
More information through EDIRC
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.:
- 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, 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.
- 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).
- Giot Pierre & Laurent Sebastien, 2001. "Modelling daily value-at-risk using realized volatility and arch type models," Research Memorandum 014, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- 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.
- 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.
- G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Oxford University Press, vol. 36(3), pages 335-346.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- 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.
- Donald W.K. Andrews, 1993.
"Empirical Process Methods in Econometrics,"
Cowles Foundation Discussion Papers
1059, Cowles Foundation for Research in Economics, Yale University.
- Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
- 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.
- 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.
- M. S. Feldstein, 1969. "Mean-Variance Analysis in the Theory of Liquidity Preference and Portfolio Selection," Review of Economic Studies, Oxford University Press, vol. 36(1), pages 5-12.
- Olivier SCAILLET, 2004. "Nonparametric Estimation of Conditional Expected Shortfall," FAME Research Paper Series rp112, International Center for Financial Asset Management and Engineering.
When requesting a correction, please mention this item's handle: RePEc:ecm:latm04:44. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)
If references are entirely missing, you can add them using this form.