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Multivariate Risk Management
Company: Humboldt-Universitat zu Berlin
Year Of Publication: 2005
Month Of Publication: February
Pages: 63
Download Count: 606
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Comment Num: 0
Language: EN
Who Can Read: Free
Date: 2-9-2006
Publisher: Administrator
In this thesis we propose a risk management methodology to high-dimensional financialportfolios. Instead of estimating the joint density of the portfolios in a high-dimensionalspace, we are encouraged by using the independent component analysis (ICA) to decomposethe dependent risk factors to a linear transformation of independent components (ICs).The marginal density and the volatility process of each IC are estimated in a univariatedimension. Thereafter the joint densities and the dependence structures of the ICs and theoriginal risk factors can be calculated using the statistical property of the independence andits linear transformation. We assume the marginal densities of ICs belong to the generalizedhyperbolic (GH) distribution family since this family possesses semi-heavy tails and mimicsthe empirical distributions of the ICs appropriately. Further we implement a nonparametricadaptive methodology to estimate the local volatilities of ICs based on a homogeneity test.In order to check the reliability of the proposed methodology, we consider a portfolio in ourstudy: a 2-dimensional exchange rates DEM/USD and GBP/USD with 4 different tradingstrategies. The empirical studies show that the performance of the VaR forecast usingthe proposed methodology is better than the popular Delta-Gamma-Normal model. Allcalculations and simulations are able to be recalculated with the software XploRe.
Chen, M.A. Ying Sign in to follow this author
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