We consider mortgages including the possibility of an unemployment insurance. The insurance company pays the cash flows of the credit as soon as the borrower becomes unemployed, for a maximal number of payments fixed in the contract. We develop a probabilistic model for describing the cash flows paid by the insurance company. We jointly take into account unemployment, job search and prepayment phenomena. With such a model it is possible to study the probabilistic properties of the cash flow pattern as a function of the age of the credit. Finally, we discuss the estimation of the parameters of such a model and its use for pricing the insurance contract.

Keywords : unemployment insurance, prepayment, duration model, pricing.

JEL : G 11.