Tid: 27 mars 2017 kl 15.15-16.00.

Föredragshållare: Carl Ljung

Titel: Copula Selection and Parameter Estimation in Market Risk Models (Master's thesis)

Abstract In this thesis, literature is reviewed for theory regarding elliptical copulas (Gaussian, Student?s t, and Grouped t) and methods for calibrating parametric copulas to sets of observations. Theory regarding model diagnostics is also summarized in the thesis. Historical data of equity indices and government bond rates from several geographical regions along with U.S. corporate bond indices are used as proxies of the most significant stochastic variables in the investment portfolio of If P&C. These historical observations are transformed into pseudouniform observations, pseudo-observations, using parametric and non-parametric univariate models. The parametric models are fitted using both maximum likelihood and least squares of the quantile function. Elliptical copulas are then calibrated to the pseudo-observations using the well known methods Inference Function for Margins (IFM) and Semi-Parametric (SP) as well as compositions of these methods and a non-parametric estimator of Kendall?s tau. The goodness-of-fit of the calibrated multivariate models is assessed in aspect of general dependence, tail dependence , mean squared error as well as by using universal measures such as Akaike and Bayesian Information Criterion, AIC and BIC. The mean squared error is computed both using the empirical joint distribution and the empirical Kendall distribution function. General dependence is measured using the scale-invariant measures Kendall?s tau, Spearman?s rho, and Blomqvist?s beta, while tail dependence is assessed using Krupskii?s tail-weighted measures of dependence (see [16]). Monte Carlo simulation is used to estimate these measures for copulas where analytical calculation is not feasible. Gaussian copulas scored lower than Student?s t and Grouped t copulas in every test conducted. However, not all test produced conclusive results. Further, the obtained values of the tail-weighted measures of dependence imply a systematically lower tail dependence of Gaussian copulas compared to historical observations.

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