Asymmetric Power Distribution: Theory and Applications to Risk Measurement
AbstractTheoretical 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
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Bibliographic InfoPaper provided by Econometric Society in its series Econometric Society 2004 Latin American Meetings with number 44.
Date of creation: 11 Aug 2004
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expected shortfall; value-at-risk; generalized power distribution;
Other versions of this item:
- Ivana Komunjer, 2007. "Asymmetric power distribution: Theory and applications to risk measurement," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(5), pages 891-921.
- 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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