Rationales of mortgage insurance premium structures

Journal of Real Estate Research, The,  1997  by Barry Dennis,  Chionglong Kuo,  Tyler T Yang

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The payments for defaulters in the Refund case are higher than those in the Upfront case, i.e., DF,RF > DF,UF. The difference between the payment made by a defaulter in the Upfront case and that in the Refund case is positively correlated with prepayment rates. A defaulter's premium payments in the Refund case reduce to those in the Upfront case when the rates of prepayment are zero. Under normal circumstances when the prepayment rates are not expected to be close to zero, a defaulter's payment in the Financing case is always below that in the Annual case. However, when prepayment rates are expected to be very low, the relative size of the premium payment between the Annual case and the Financing case depends upon the time of default. Early defaulters pay lower premium in the Financing case than in the Annual case but the late defaulters pay higher premium in the Financing case than in the Annual case. Prepayers. Borrower premium payments in the Refund case (PP,RF) are lower than those in the Annual case (pp,AN) if the prepayment occurs in the early and late policy years, but may become larger than those in the Annual case if the prepayment occurs during the periods of high default probability. PPt' is also lower than DF,RF and approaches it as t approaches T . The prepayers always pay more in the Financing case than in the Upfront case because insurers lose the unamortized premium balance in the Financing case once default occurs. The premium payments in the Annual case and the Refund case are lower than those in the Upfront case and the Financing case for early prepayers but higher for late prepayers.

Numerical Results

To illustrate the above framework and compare the alternative premium programs, we constructed numerical examples. The underlying conditional prepayment and default rates used to determine the fair insurance premium rates for the four programs are reported in Price Waterhouse LLP (1997). The actual FHA default and prepayment experience is computed for policy years 1 to 22 and the remaining years are estimated with grouped logit models. The rates are estimated by taking a simple average across all thirty-year fixed-rate mortgages for each policy year. The resulting default and prepayment rates are displayed in Exhibit 1.

Given the conditional prepayment and default rates, we calculated the premium schedule for each structure case assuming zero net present values for the insurers and a claim loss rate of 40% of the remaining principal balance. Expressed as a percentage of the initial loan amount, the premium rates are 0.55% per annum for the Annual case, 3.36% for the Upfront case, 4.04% for the Refund case, and 3.76% for the Financing case.

Borrower's Perspective: Comparison of Alternative Premium Paid by Premium Structures Exhibits 2 and 3 display the present value of the ex-post premium payments for prepayers and defaulters, respectively, by year of termination. The dramatic difference in total premiums paid, depending upon year of termination and premium program, is apparent in these exhibits. These differences in total premiums paid provide incentives for borrowers to select the most financially advantageous program, i.e., the program with lowest total cost. Which program is most attractive to a prepayer depends upon the year in which termination occurs.