In this paper, we propose a simple non-parametric goodness-of-fit test for elliptical copulas of any dimension. It is based on the equality of Kendall’s tau and Blomqvist’s beta for all bivariate margins. Nominal level and power of the proposed test are investigated in a Monte Carlo study. An empirical application illustrates our goodness-of-fit test at work.

A sound statistical model for recovery rates is required for various applications in quantitative risk management, with the computation of capital requirements for loan portfolios as one important example. We compare different models for predicting the recovery rate on borrower level including linear and quantile regressions, decision trees, neural networks, and mixture regression models. We fit and apply these models on the worldwide largest loss and recovery data set for commercial loans provided by GCD, where we focus on small- and medium-sized entities in the US. Additionally, we include macroeconomic information via a predictive Crisis Indicator or Crisis Probability indicating whether economic downturn scenarios are expected within the time of resolution. The horserace is won by the mixture regression model which regresses the densities as well as the probabilities that an observation belongs to a certain component.

Recently, several copula-based approaches have been proposed for modeling stationary multivariate time series. All of them are based on vine copulas, and they differ in the choice of the regular vine structure. In this article, we consider a copula autoregressive (COPAR) approach to model the dependence of unobserved multivariate factors resulting from two dynamic factor models. However, the proposed methodology is general and applicable to several factor models as well as to other copula models for stationary multivariate time series. An empirical study illustrates the forecasting superiority of our approach for constructing an optimal portfolio of U.S. industrial stocks in the mean-variance framework.

This study on explaining aggregated recovery rates (ARR) is based on the largest existing loss and recovery database for commercial loans provided by Global Credit Data, which includes defaults from 5 continents and over 120 countries. The dependence of monthly ARR from bank loans on various macroeconomic factors is examined and sources of their variability are stated. For the first time, an influence of stochastically estimated monthly growth of GDP USA and Europe is quantified. To extract monthly signals of GDP USA and Europe, dynamic factor models for panel data of different frequency information are employed. Then, the behavior of the ARR is investigated using several regression models with unshifted and shifted explanatory variables in time to improve their forecasting power by taking into account the economic situation after the default. An application of a Markov switching model shows that the distribution of the ARR differs between crisis and prosperity times. The best fit among the compared models is reached by the Markov switching model. Moreover, a significant influence of the estimated monthly growth of GDP in Europe is observed for both crises and prosperity times.