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This study examines the rationales for the design of mortgage insurance premium structures. The actuarially sound premium prices of several widely used structures are formally derived. Two types of cross-subsidization are identified in different structures: (1) subsidization across termination years and (2) extra-subsidization of defaulters by nondefaulters. Because these two types of subsidization exist to different degree among the structures, a borrower may self-select into certain structures to maximize (minimize) the benefits (losses) of cross-subsidies. Adverse selection arises when the borrower’s characteristics cannot be completely observed by the insurer. The actuarially sound premium prices should be adjusted for such adverse selection behaviors. Numerical examples are provided to illustrate such adjustments.
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Dennis et al. (1997) studied this question.
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