Interest rates modeling for insurance : interpolation, extrapolation, and forecasting.

Summary The ORSA Own Risk Solvency and Assessment is a set of rules defined by the European Solvency II directive. It is intended to serve as a decision support tool and strategic risk analysis. In the context of the ORSA, insurance companies must assess their future solvency, on an ongoing and prospective basis. In order to do so, they must obtain projections of their balance sheet (assets and liabilities) over a certain time horizon. In this thesis, we focus mainly on the aspect of predicting future asset values. More precisely, we deal with the yield curve, its construction and extrapolation at a given date, and its predictions envisaged in the future. In the text, we refer to the "yield curve", but it is in fact the construction of discount factor curves. Counterparty default risk is not explicitly addressed, but techniques similar to those developed can be adapted to the construction of rate curves incorporating counterparty default risk.