GHICA - Risk analysis with GH distributions and independent components

Ying Chen, Wolfgang Härdle, Vladimir Spokoiny

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


Over recent years, a 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.

Original languageEnglish
Pages (from-to)255-269
Number of pages15
JournalJournal of Empirical Finance
Issue number2
Publication statusPublished - Mar 2010
Externally publishedYes


  • Expected shortfall
  • Generalized hyperbolic distribution
  • Independent component analysis
  • Local exponential estimation
  • Multivariate risk management
  • Value at risk


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