*Tid:* **27 mars 2017 kl 15.15-16.00.**
**Seminarierummet 3721**, Institutionen för
matematik, KTH, Lindstedtsvägen 25, plan 7.
Karta!
*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.
The full report (pdf)
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