Even taking into account the randomness coming from calculating value of a bond in case of default, VaR of our portfolio calculated by following conventional Credit Metrics approach is more optimistic in comparison with VaR computed using Copula approach. The difference might be insignificant in particular case, but it potentially might cause problems when working with large portfolios.
4. Conclusion
In this project Copula functions were integrated to Credit Metrics methodology of credit risk modelling. Following Asset value approach, dependence structure of joint credit rating movements was modelled using asset returns of issuser companies. As it turned out t-distributions were best to describe asset returns of our companies. By means of pair-copula constrution method results in Table 4 were yielded. It turned out that asset returns of Lukoil, Gazprom and Norilsk Nickel posses positive dependence structure. Moreover, there are upper and lower tail dependence between each pair representing degree to which returns might take extreme values jointly. From modelled joint distribution 3305 random points were generated in order to perform Monte Carlo simulation of possible joint asset returns. Those values were exploited to obtain possible values of our portfolio in one year. Then VaR percentile was estimated at different confidence levels.
5. Suggestions for further research
As it was mentioned above, pair-copula construction is only one of the ways of modelling multidimensional joint distribution by using copulas. So another method might be used to model joint distribution of asset returns. Moreover, R implementation of pair-copula construction has 40 copula types to be fitted, and the best fit was chosen by Goodnes-of-fit test. Thus, increasing number of implemented copulas might result in a better fit. Concerning input parameters, real forward-zero rates can be used to make a complete analysis of the portfolio. Additionally, a test can be performed to figure out whether the differences of VaR's found in Table 5 are statistically significant.