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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If pricing does not take self-selection into account, and estimation of the resulting net present values ignores self-selection as well, the results indicate that premiums just about cover claim costs for each program, with the Upfront program and the Financing program being slightly negative and the other two programs being slightly positive (see the top bank of numbers). If the effect of deterministic pricing is measured properly, taking into account that borrowers will self-select, it becomes apparent that some programs will be significant losers (have negative net present value) and others may be significant gainers (second from top bank of numbers). As expected, the two programs preferred by the majority of defaulters (the Annual program and the Financing program) are the programs at most financial risk due to adverse selection, having -0.48 and -0.88 net present values. Of course, if prices are set taking into account the self-selection of borrowers, and the measurement of the results also takes self-selection into account, then each program's prices exactly cover total claims cost, and the mean net present value is zero for all programs.

Exhibits 8 and 9 display the effect of incorporating self-selection in pricing on the total present value of premium payments by non-defaulters and defaulters by termination year (the equivalent of Exhibits 2 and 3). As expected, the profile of the total premium paid curves is not changed by the premium adjustment, since the adjustment is essentially a level adjustment and not a time pattern adjustment. For both non-defaulters and defaulters, the total premium curves for the programs preferred by defaulters (the Annual case and the Financing case) shift upward, reflecting the higher premium that is charged for these programs when self-selection is taken into account. Similarly, the curves for the programs preferred by non-defaulters shift downwards relative to pricing that does not take self-selection into account.

Conclusions

In this study, we develop a framework for determining the premium structure of mortgage insurance. Mortgage insurance has the unique features of being a contract with multi-period coverage, finite life, decreasing risk over time, and high systematic (catastrophic) risk, and is a mandatory contract to cover the risk to the lender (instead of the borrower who pays the premium). Because of these unique features, the existing insurance theories and premium structures in other types of insurance may not be applicable. The framework we developed allows the insurer to calculate the premium amount needed to cover the expected claim cost and earn economic profit. The rationale of different premium structures is analyzed as a mechanism to address the problem of adverse selection caused by the information asymmetry between the lender and borrower regarding the borrower's tenure plan and level of default risk. With the combination of upfront premiums, annual premiums and premium refunds, it is possible to reduce the degree of cross-subsidy from stable borrowers to mobile borrowers and from low-risk borrowers to high-risk borrowers. However, upfront premiums tend to increase homebuyer downpayment burdens and decrease housing affordability. For most mortgage insurers with a social mission, the amount of upfront premiums to charge would depend on the trade-off between economic and social benefits.