Evgenia Ageeva: Bayesian Inference for Multivariate t Copulas Modeling Financial Market Risk

Adviser: Prof. Dr. Peter Bühlmann

Co-Adviser Dr. Martin Mächler

Sepember 2011

Abstract:

The main objective of this thesis is to develop a Markov chain Monte Carlo (MCMC) method under the Bayesian inference framework for estimating meta-t copula functions for modeling financial market risks. The complete posterior distribution of the copula parameters resulting from Bayesian MCMC allows further analysis such as calculating the risk measures that incorporate the parameter uncertainty. The simulation study of the fictitious and real equity portfolio returns shows that the parameter uncertainty tends to increase the risk measures, such as the Value-at-Risk and the Expected Shortfall of the profit-and-loss distribution.

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