The Cost of Delay in a Mortgage/Credit Loan Portfolio

Using an actuarial model, we examine the cost of delay in mortgage/credit loan payments. It is assumed that the default arrival process follows the Poisson process and the loss sizes are assumed to be independent and an identical truncated exponential. We also assume that the delay between default occurrence and partially (or fully) recovered payment is an independent identical truncated exponential random variable. For the recovery rate random variable, we simply use its expectation. Using the relationship between the shot noise process and accumulated/discounted aggregate losses process and applying the piecewise deterministic Markov processes theory, we obtain the explicit expressions for the expected value of losses and the expected value of part (or whole) of the loan recovered with the delay. Based on these moments, we define and predict the cost of delay in a mortgage/credit loan portfolio and their numerical examples are provided.