You are here

High Dimensional Dependence Modeling Using Vine Copulas

Professor: 
Type: 
Master's Thesis
Corporate Partner: 
Zurich Insurance Company Ltd
Date Published: 
October 6, 2014

This Master’s thesis topic arose from the methodological problems concerning dependence modeling in a country risk tool developed by Zurich Insurance Group. The tool — namely, the Zurich Risk Room (ZRR) — is a corporate-customer product which aims to inform users regarding the ranking of 160 countries using 72 risk indicators. Users are allowed to choose fewer risk indicators in which they are interested and view a global risk map of 160 countries. In this respect the first feature of the tool is to compare the riskiness of countries with respect to chosen risk indicators. The ZRR further enables users to examine a “what if?” scenario. Users are allowed to change a risk indicator of one country and observe its effects on the overall ranking. In the current version of the tool, the effect of a change in one factor on the other factors is computed using an expert opinion matrix which reflects the causalities of risk indicators. We focus on dependence modeling via copulas in order to define coherent “what if?” scenarios which will turn into the construction of coherent stress tests. It is essential to notice that analyzing dependence in this country risk tool involves both risk factor relations within a country (i.e., analyzing the effects of a risk factor change for the country chosen) and country interdependence (i.e., analyzing the effects of a change in a country risk for other countries). Due to the number of countries (160) and risk indicators (72), the method of expressing dependencies within the ZRR concerns high dimensional dependence modeling. For this, we focus on vine copulas which are introduced as a new graphical method for high dimensional data developed in Bedford and Cooke (2002).

We further provide a probabilistic approach to coherent stress testing using Bayesian nets. Section 6 explains a possible application of dependence modeling for the ZRR by dividing the dependence problem for the scenario analysis into two parts. The first part comprises modeling the dependence of the risk indicators of one country using vine copulas and observing the effect of a change in one indicator. The second part defines a model to reflect the interconnectedness of countries, using sovereign CDS spreads. A study of 13 countries is carried out in order to reflect their interdependencies. Finally, using the resulting interdependence structure for 13 countries, a conditional interdependence impact simulation study is performed.This Master’s thesis topic arose from the methodological problems concerning dependence modeling in a country risk tool developed by Zurich Insurance Group. The tool — namely, the Zurich Risk Room (ZRR) — is a corporate-customer product which aims to inform users regarding the ranking of 160 countries using 72 risk indicators. Users are allowed to choose fewer risk indicators in which they are interested and view a global risk map of 160 countries. In this respect the first feature of the tool is to compare the riskiness of countries with respect to chosen risk indicators. The ZRR further enables users to examine a “what if?” scenario. Users are allowed to change a risk indicator of one country and observe its effects on the overall ranking. In the current version of the tool, the effect of a change in one factor on the other factors is computed using an expert opinion matrix which reflects the causalities of risk indicators. We focus on dependence modeling via copulas in order to define coherent “what if?” scenarios which will turn into the construction of coherent stress tests. It is essential to notice that analyzing dependence in this country risk tool involves both risk factor relations within a country (i.e., analyzing the effects of a risk factor change for the country chosen) and country interdependence (i.e., analyzing the effects of a change in a country risk for other countries). Due to the number of countries (160) and risk indicators (72), the method of expressing dependencies within the ZRR concerns high dimensional dependence modeling. For this, we focus on vine copulas which are introduced as a new graphical method for high dimensional data developed in Bedford and Cooke (2002).

We further provide a probabilistic approach to coherent stress testing using Bayesian nets. Section 6 explains a possible application of dependence modeling for the ZRR by dividing the dependence problem for the scenario analysis into two parts. The first part comprises modeling the dependence of the risk indicators of one country using vine copulas and observing the effect of a change in one indicator. The second part defines a model to reflect the interconnectedness of countries, using sovereign CDS spreads. A study of 13 countries is carried out in order to reflect their interdependencies. Finally, using the resulting interdependence structure for 13 countries, a conditional interdependence impact simulation study is performed.This Master’s thesis topic arose from the methodological problems concerning dependence modeling in a country risk tool developed by Zurich Insurance Group. The tool — namely, the Zurich Risk Room (ZRR) — is a corporate-customer product which aims to inform users regarding the ranking of 160 countries using 72 risk indicators. Users are allowed to choose fewer risk indicators in which they are interested and view a global risk map of 160 countries. In this respect the first feature of the tool is to compare the riskiness of countries with respect to chosen risk indicators. The ZRR further enables users to examine a “what if?” scenario. Users are allowed to change a risk indicator of one country and observe its effects on the overall ranking. In the current version of the tool, the effect of a change in one factor on the other factors is computed using an expert opinion matrix which reflects the causalities of risk indicators. We focus on dependence modeling via copulas in order to define coherent “what if?” scenarios which will turn into the construction of coherent stress tests. It is essential to notice that analyzing dependence in this country risk tool involves both risk factor relations within a country (i.e., analyzing the effects of a risk factor change for the country chosen) and country interdependence (i.e., analyzing the effects of a change in a country risk for other countries). Due to the number of countries (160) and risk indicators (72), the method of expressing dependencies within the ZRR concerns high dimensional dependence modeling. For this, we focus on vine copulas which are introduced as a new graphical method for high dimensional data developed in Bedford and Cooke (2002).

We further provide a probabilistic approach to coherent stress testing using Bayesian nets. Section 6 explains a possible application of dependence modeling for the ZRR by dividing the dependence problem for the scenario analysis into two parts. The first part comprises modeling the dependence of the risk indicators of one country using vine copulas and observing the effect of a change in one indicator. The second part defines a model to reflect the interconnectedness of countries, using sovereign CDS spreads. A study of 13 countries is carried out in order to reflect their interdependencies. Finally, using the resulting interdependence structure for 13 countries, a conditional interdependence impact simulation study is performed.This Master’s thesis topic arose from the methodological problems concerning dependence modeling in a country risk tool developed by Zurich Insurance Group. The tool — namely, the Zurich Risk Room (ZRR) — is a corporate-customer product which aims to inform users regarding the ranking of 160 countries using 72 risk indicators. Users are allowed to choose fewer risk indicators in which they are interested and view a global risk map of 160 countries. In this respect the first feature of the tool is to compare the riskiness of countries with respect to chosen risk indicators. The ZRR further enables users to examine a “what if?” scenario. Users are allowed to change a risk indicator of one country and observe its effects on the overall ranking. In the current version of the tool, the effect of a change in one factor on the other factors is computed using an expert opinion matrix which reflects the causalities of risk indicators. We focus on dependence modeling via copulas in order to define coherent “what if?” scenarios which will turn into the construction of coherent stress tests. It is essential to notice that analyzing dependence in this country risk tool involves both risk factor relations within a country (i.e., analyzing the effects of a risk factor change for the country chosen) and country interdependence (i.e., analyzing the effects of a change in a country risk for other countries). Due to the number of countries (160) and risk indicators (72), the method of expressing dependencies within the ZRR concerns high dimensional dependence modeling. For this, we focus on vine copulas which are introduced as a new graphical method for high dimensional data developed in Bedford and Cooke (2002).

We further provide a probabilistic approach to coherent stress testing using Bayesian nets. Section 6 explains a possible application of dependence modeling for the ZRR by dividing the dependence problem for the scenario analysis into two parts. The first part comprises modeling the dependence of the risk indicators of one country using vine copulas and observing the effect of a change in one indicator. The second part defines a model to reflect the interconnectedness of countries, using sovereign CDS spreads. A study of 13 countries is carried out in order to reflect their interdependencies. Finally, using the resulting interdependence structure for 13 countries, a conditional interdependence impact simulation study is performed.