Rationales of mortgage insurance premium structures

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

In summary, early prepayers (through year 7) will tend to choose either the Annual case or the Refund case, while later prepayers will prefer the Upfront case. All but the latest defaulters (after year 22) will tend to choose the Financing case. The latest defaulters, like prepayers, will choose the Upfront case.

Insurer's Perspective: Alternative Premium Structure and Adverse Selection

The financial effect of the different premium structures on insurers will depend on the revenues generated relative to the claim costs incurred. While the claim costs are independent of the premium structure (absent ancillary or feedback effects), the revenues depend upon the combination of the prepayment and default patterns, and the premium structure. To evaluate the financial effect, we construct a set of nine types of prepayment/default patterns based upon the FHA portfolio. The nine types comprise combinations of low, medium and high rates for both prepayments and defaults. Medium rates are FHA average conditional prepayment and default rates. High rates are 150% of medium, and low rates are 50% of medium. The same mix of borrowers is used for each premium program. Premium levels are calculated such that total premium payments generate zero net (of claim costs) present value under the average FHA prepayment and default rates (the medium prepayment/medium default case). Exhibit 4 presents revenues (expressed as a percent of original principal balance) for each of the termination combinations and for each premium program, as well as claim costs for each termination combination. The means and standard deviations are also presented. Exhibit 5 presents the net present value of the different premium programs by termination combination. Because premiums were set based upon average defaults and prepayments, the net present value of the medium default/medium prepayment (M Def M Prep) case is zero for all premium programs. If borrowers are evenly distributed among the nine termination rate categories, the nonlinearity of revenues with regard to the termination profiles results in average net present value across all termination combinations different from zero. In other words, pricing based upon the mean only, not taking into account the variance, results in biased pricing.