This paper studies the empirical quantification of basis risk in the context of index-linked hedging strategies. Basis risk refers to the risk of non-payment of the index-linked instrument, given that the hedger’s loss exceeds some critical level. The quantification of such risk measures from empirical data can be done in various ways and requires special consideration of the dependence structure between the index and the company’s losses as well as the estimation of the tails of a distribution. In this context, previous literature shows that extreme value theory can be superior to traditional methods with respect to estimating quantile risk measures such as the value at risk. Thus, the aim of this paper is to conduct an empirical analysis of basis risk using multivariate extreme value theory and extreme value copulas to estimate the underlying risk processes and their dependence structure in order to obtain a more adequate picture of basis risk associated with index-linked hedging strategies. Our results emphasize that the application of extreme value theory leads to better fits of the tails of the marginal distributions in the considered stock price sample and that traditional methods in regard to estimating marginal distributions tend to overestimate basis risk, while basis risk can in contrast be higher when taking into account extreme value copulas.

We extend the linear quantile regression with a neural network structure to enable more flexibility in every quantile of the bank loan loss given default distribution. This allows us to model interactions and non-linear impacts of any kind without the need of specifying the exact form beforehand. The precision of the quantile forecasts increases up to 30% compared to the benchmark, especially for higher quantiles which are most important in credit risk. By using a novel feature importance measure, we calculate the strength, direction, interactions and other non-linear impacts for every conditional quantile and every variable. This enables us to explain why our extension exhibits superior performance over the benchmark. Moreover, we find that the macroeconomy is up to two times more important in USA than in Europe and has large joint impacts in both regions. The macroeconomy is most important in the US, whereas in Europe collateralization is essential.

Resolution of non-performing loans is a key determinant of bank credit default losses. This paper analyzes macroeconomic and systematic frailty effects of the default resolution time for a sample of 17,395 defaulted bank loans in USA, Great Britain, and Canada. We find that frailties have a huge impact on the resolution times. In a representative sample portfolio, median resolution times more than double in a recession when compared to an expansion. This leads to highly skewed distributions of losses and considerable systematic risk of the bank portfolio.