### Dependence modeling using EVT and D-Vine

#### Abstract

*Extreme occurrences such as extreme gains and extreme losses in financial market are unavoidable. Accurate knowledge of dependence on these extremes can help investors to adjust their portfolio mix accordingly. This paper therefore focuses on modeling dependence in extreme gains and losses in a portfolio consisting of three assets using D-Vine Copula. The concept of extreme value theory, the peak over threshold approach is use to identify the sets of extreme gains and extreme losses in each asset contain in the portfolio. For the three assets, a total of six sets (3 sets of extreme gains and 3 sets of extreme losses) are use in the dependence modeling. Due to the well known fact that financial return series are not independent and identically distributed (i.i.d), the returns are first filtered using a GARCH-type model before the extreme value analysis. To take into account the different types of dependence normally present in financial return series, the D-Vine copula, is use to model the dependence structure in the sets of extremes for all the assets in the portfolio. Empirical evidence using D-Vine copula for the dependence modeling, indicates that the conditional and unconditional dependence parameters are significantly different from zero for all pairs of tails. Some of these dependence parameters are negative, showing that an extreme gain in one asset may lead to an extreme loss in the other asset vice versa.*

**ABSTRACT: ***Extreme occurrences such as extreme gains and extreme losses in financial market are unavoidable. Accurate knowledge of dependence on these extremes can help investors to adjust their portfolio mix accordingly. This paper therefore focuses on modeling dependence in extreme gains and losses in a portfolio consisting of three assets using D-Vine Copula. The concept of extreme value theory, the peak over threshold approach is use to identify the sets of extreme gains and extreme losses in each asset contain in the portfolio. For the three assets, a total of six sets (3 sets of extreme gains and 3 sets of extreme losses) are use in the dependence modeling. Due to the well known fact that financial return series are not independent and identically distributed (i.i.d), the returns are first filtered using a GARCH-type model before the extreme value analysis. To take into account the different types of dependence normally present in financial return series, the D-Vine copula, is use to model the dependence structure in the sets of extremes for all the assets in the portfolio. Empirical evidence using D-Vine copula for the dependence modeling, indicates that the conditional and unconditional dependence parameters are significantly different from zero for all pairs of tails. Some of these dependence parameters are negative, showing that an extreme gain in one asset may lead to an extreme loss in the other asset vice versa.*

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