The purpose of this seminar is to give you a good understanding of the use of multivariate statistics and Extreme Value modelling in quantifying and managing risk.
We start with a general introduction to multivariate statistics and analysis. We give an overview of the applications of multivariate modelling in finance, and we explain the basics of correlation and correlation analysis.
We then explain and demonstrate how you can use multiple regression analysis to determine relationships between economic and financial variables, and we explain the use "discriminant analysis" to compute linear predictors from sets of normally distributed data to allow for classification of new observations.
Further, we explain and show how sampling from multivariate return distributions can be performed and how "Value-at-Risk" can be derived from a total portfolio loss distribution that is generated using simulation techniques. We also explain how you can overcome the assumptions about normally distributed returns by using GARCH techniques to project volatilities from historical data.
We also explain and demonstrate how principal components analysis can be used to determine a smaller set of "synthetic" variables that could explain the original set (for example variations in the yield curve).
We then introduce Extreme Value Theory and explain and demonstrate its applications in finance.
We present the two main approaches to estimating tail distributions: the "Block Maxima" and the "Peaks over Threshold" groups of models. Emphasis will be on the practical day-to-day applications of these models, rather than on their theoretical mathematical properties. We demonstrate how a "Generalized Pareto Distribution" can be fitted to real-life financial data (stock prices etc.), and we visualize results using graphical tools.
We then turn to look at how EVT can be used in financial risk management. We discuss the opportunities and pitfalls of using EVT. We use extreme value theory to calculate conditional and non-conditional VaR, and we compare these measures with the VaR measures obtained using e.g. normal distribution assumptions. Finally, we discuss the use of EVT in "Stress Testing", in quantifying operational risks, and in asset allocation.