Modeling Cycle Dependence in Credit Insurance

Abstract

Abstract:Business and credit cycles have an impact on credit insurance, as they do on other businesses. Nevertheless, in credit insurance, the impact of the systemic risk is even more important and can lead to major losses during a crisis. Because of this, the insurer surveils and manages policies almost continuously. The management actions it takes limit the consequences of a downturning cycle. However, the traditional modeling of economic capital does not take into account this important feature of credit insurance. This paper proposes a model aiming to estimate future losses of a credit insurance portfolio, while taking into account the insurer's management actions. The model considers the capacity of the credit insurer to take on less risk in the case of a cycle downturn, but also the inverse, in the case of a cycle upturn; so, losses are predicted with a more dynamic perspective. According to our results, the economic capital is over-estimated when not considering the management actions of the insurer.

Rating Transitions Forecasting: A Filtering Approach

“…Knowing that {Θ n−1 = h, Y n = y n }, we assume that the conditional distribution of the random variable ∆N n is binomial with parameters (y n , L h ). Similar settings can be found in [7] and [25].…”

“…For the sake of completeness, we provide in Appendix B a self-consistent proof yielding a general explicit filtering formula with no simultaneous jumps. Then, we provide in Appendix B.3, the adequate adaptations for the rating migration context to obtain the filtering equation (7).…”

“…This part aims to explain how to adapt continuous filtering to discrete rating migration framework. We propose an adaptation of the calibration algorithm in order to be compliant with the continuous filtering formula (7). Previous adaptations done for the discrete framework are still required but are not sufficient: Baum-Welch algorithm is an estimation in discrete time which is not compliant with the continuous version of the filter.…”