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Title:GHICA: Risk analysis with GH distributions and independent components PDF Logo
Authors:Chen, Ying
Härdle, Wolfgang Karl
Spokoiny, Vladimir
Issue Date:2006
Series/Report no.:SFB 649 discussion paper 2006,078
Abstract:Over 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.
Subjects:multivariate risk management
independent component analysis
generalized hyperbolic distribution
local exponential estimation
value at risk
expected shortfall
JEL:C14
C16
C32
C61
G20
Document Type:Working Paper
Appears in Collections:SFB 649 Discussion Papers, HU Berlin

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