GHICA - Risk Analysis with GH Distributions and Independent Components
AbstractOver recent years, study on risk management has been prompted by the Basel committee for regular banking supervisory. There are however limitations of some widely-used risk management methods that either calculate risk measures under the Gaussian distributional assumption or involve numerical difficulty. The primary aim of this paper is to present a realistic and fast method, GHICA, which overcomes the limitations in multivariate risk analysis. The idea is to first retrieve independent components (ICs) out of the observed high-dimensional time series and then individually and adaptively fit the resulting ICs in the generalized hyperbolic (GH) distributional framework. For the volatility estimation of each IC, the local exponential smoothing technique is used to achieve the best possible accuracy of estimation. Finally, the fast Fourier transformation technique is used to approximate the density of the portfolio returns. The proposed GHICA method is applicable to covariance estimation as well. It is compared with the dynamic conditional correlation (DCC) method based on the simulated data with d = 50 GH distributed components. We further implement the GHICA method to calculate risk measures given 20-dimensional German DAX portfolios and a dynamic exchange rate portfolio. Several alternative methods are considered as well to compare the accuracy of calculation with the GHICA one.
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Bibliographic InfoPaper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-078.
Length: 32 pages
Date of creation: Nov 2006
Date of revision:
Multivariate Risk Management; Independent Component Analysis; Generalized Hyperbolic Distribution; Local Exponential Estimation; Value at Risk; Expected Shortfall.;
Other versions of this item:
- Chen, Ying & Härdle, Wolfgang & Spokoiny, Vladimir, 2010. "GHICA -- Risk analysis with GH distributions and independent components," Journal of Empirical Finance, Elsevier, vol. 17(2), pages 255-269, March.
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- G20 - Financial Economics - - Financial Institutions and Services - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-11-25 (All new papers)
- NEP-ECM-2006-11-25 (Econometrics)
- NEP-RMG-2006-11-25 (Risk Management)
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