Value at risk : coherent properties within the class of elliptical distributions and estimation procedures

Abstract

In this thesis, we shall focus on elliptical distributions and the connections to riskmeasurement. We shall present the connection between ellipt ical and sphericaldistributions and provide algorithms for data simulations from this class ofdistributions. We will further present the axiomatic framework for coherent riskmeasures and prove why Value at Risk is not a coherent risk measure. We shall est imateand compute Value at Risk via quant ile, historical simulations methodology andparametric methodology. Finally, we shall compare historical and parametricsimulations of VaR for a portfolio contained of three assets.