GHICA - Risk Analysis with GH Distributions and Independent Components

SFB 649 Discussion Paper 2006-078

32 Pages Posted: 9 Jan 2017

See all articles by Ying Chen

Ying Chen

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Wolfgang K. Härdle

Blockchain Research Center; Xiamen University - Wang Yanan Institute for Studies in Economics (WISE); Charles University; National Yang Ming Chiao Tung University; Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

V. Spokoiny

Weierstras Institute for Applied Analysis and Stochastics (WIAS)

Date Written: November 16, 2006

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.

Keywords: Multivariate Risk Management, Independent Component Analysis, Generalized Hyperbolic Distribution, Local Exponential Estimation, Value at Risk, Expected Shortfall.

JEL Classification: C14, C16, C32, C61, G20

Suggested Citation

Chen, Ying and Härdle, Wolfgang K. and Spokoiny, Vladimir, GHICA - Risk Analysis with GH Distributions and Independent Components (November 16, 2006). SFB 649 Discussion Paper 2006-078, Available at SSRN: https://ssrn.com/abstract=2894368 or http://dx.doi.org/10.2139/ssrn.2894368

Ying Chen

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Spandauer Strasse 1
Berlin, D-10178
Germany

Wolfgang K. Härdle (Contact Author)

Blockchain Research Center ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE) ( email )

A 307, Economics Building
Xiamen, Fujian 10246
China

Charles University ( email )

Celetná 13
Dept Math Physics
Praha 1, 116 36
Czech Republic

National Yang Ming Chiao Tung University ( email )

No. 1001, Daxue Rd. East Dist.
Hsinchu City 300093
Taiwan

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Unter den Linden 6
Berlin, D-10099
Germany

Vladimir Spokoiny

Weierstras Institute for Applied Analysis and Stochastics (WIAS) ( email )

Mohrenstr. 39
Berlin, 10117
Germany

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