A hierarchical model of tail dependent asset returns for assessing portfolio credit risk
AbstractThis paper introduces a multivariate pure-jump Lévy process which allows for skewness and excess kurtosis of single asset returns and for asymptotic tail dependence in the multivariate setting. It is termed Variance Compound Gamma (VCG). The novelty of my approach is that, by applying a two-stage stochastic time change to Brownian motions, I derive a hierarchical structure with different properties of inter- and intra-sector dependence. I investigate the properties of the implied static copula families and come to the conclusion that they are ordered with respect to their parameters and that the lower-tail dependence of the intra-sector copula is increasing in the absolute values of skewness parameters. Furthermore, I show that the joint characteristic function of the VCG asset returns can be explicitly given as a nested Archimedean copula of their marginal characteristic functions. Applied to credit portfolio modelling, the framework introduced results in a more conservative tail risk assessment than a Gaussian framework with the same linear correlation structure, as I show in a simulation study. To foster the simulation efficiency, I provide an Importance Sampling algorithm for the VCG portfolio setting. --
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Bibliographic InfoPaper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 2: Banking and Financial Studies with number 2011,16.
Date of creation: 2011
Date of revision:
Portfolio Credit Risk; Stochastic Time Change; Brownian Subordination; Jumps; Tail Dependence; Hierarchical Dependence Structure;
Find related papers by JEL classification:
- C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
- G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-05-22 (All new papers)
- NEP-CMP-2012-05-22 (Computational Economics)
- NEP-ECM-2012-05-22 (Econometrics)
- NEP-RMG-2012-05-22 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Carlo Acerbi & Dirk Tasche, 2001. "Expected Shortfall: a natural coherent alternative to Value at Risk," Papers cond-mat/0105191, arXiv.org.
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