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T. Miazhynskaia:
"Markov Chain Monte Carlo methods and their application in financial modelling";
Talk: Seminar Finanz- und Versicherungsmathematik, TU München, München, Deutschland (invited); 2004-07-15.

Markov chain Monte Carlo (MCMC) methods are modern computational methods which can be used for the analysis of complex statistical models. We will shortly discuss fundamental theoretical concepts of MCMC methodology in the framework of Bayesian data analysis. But the main emphasis of the talk will be placed on the practical application of MCMC techniques in financial modelling. On the example of GARCH-type models with different types of conditional distribution
we will illustrate the Bayesian estimation procedure via MCMC and compare the estimation results with the ones from classical analysis. We will also consider the Bayesian measure of Value-at-Risk (VaR) and show how MCMC helps to account for parameter and model uncertainty in VaR estimates.