Unemployment insurance and mortgages

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.