Contribution to the measurement of liabilities and capital requirements for a credit insurer.

Summary The new Solvency 2 regulatory standards have a very important impact on credit insurance. The objective of this directive is that insurance companies better measure the different risks they face, so that they can build up sufficient capital to face crisis situations. Our work focuses on a rather specific insurance activity: credit insurance. Under Solvency 2, most credit insurers will move towards the development of internal models in order to better estimate their capital requirements. The objective of our study is to propose, or to give avenues for improvement of one type of internal model. First, we present a general overview of the credit insurance business and then we approach the subject of an internal model. We will then present the model we have chosen to use, a multifactor model associated with the Merton approach. We will also compare the methods for integrating correlations between counterparties in the Solvency 2 standards with that of the internal model. We will then try to refine the internal model in order to take into account an important characteristic of credit insurance: the management of guarantees (limits), which as we will see induces a decrease in capital requirements. To do so, we will introduce the consideration of credit cycles for the calculation of losses, a model that is no longer monoperiodic, as is usually the case, but with two periods. We will then present the results obtained with this model. We will then present an alternative approach using the piecewise linear approximation method via Monte Carlo simulations (PLMC). The aim here is to move from a discrete to a continuous model. We then compare the Gaussian and Student dependence structures to see what the change in this structure would mean for the capital requirements. Finally, we will look at the problem of finding high quantiles and studying the convergence of our variables. To do so, we will first introduce the measure of the market price of risk, and we will present an estimate of this market price of risk, more specifically for interest rate risk. This will allow us to obtain the dynamics of rates in a risk neutral universe. We will then address the issue of calculating the Best Estimate, in a framework of dependence between interest rate and credit risks. The calculation of the SCR will follow. We will discuss an alternative approach for calculating the capital requirement, an approach specific to structural models and which would make it possible to do without simulations for this calculation. Finally, we will conclude our study by exposing the different issues of this thesis as well as the contributions made, and the problems encountered during the work.