Longevity risk management and valuation of derivative products.

Summary In this thesis, we propose to study the longevity risk and its impact on insurers and pension plan providers. In the first part, we focus on the different mortality models. Based on this literature review, we propose an extension of the so-called CBD model, using Lévy processes, which will take into account the effects of jumps in the mortality curve. In the second part of the thesis, this new model will be used as a basis for the valuation of longevity derivatives. We use as valuation measures the so-called Wang and Esscher transforms that we will have previously defined and justified as being martingale measures equivalent to the historical measure. Finally, we propose a new contract called "mortality collar" which, by its definition, allows an efficient hedge against longevity/mortality risk, both for an insurer and for a pension fund. We provide an in-depth analysis of this risk management tool, both in its mechanism and in its valuation.