Rationales of Mortgage Insurance Premium Structures

Article excerpt

Rationales of Mortgage Insurance Premium Structurest

Abstract. 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.


Currently, different premium structures are used by various insurance/guarantee agencies, such as the Federal Housing Administration (FHA), Veteran's Administration (VA), Federal National Mortgage Association (Fannie Mae), Federal Home Loan Mortgage Corporation (Freddie Mae), and private mortgage insurance companies (PMIs). These insurance programs charge combinations of upfront and annual premiums, and premium refunds are provided when a loan is prepaid within a relatively short period of time. Given these different structures, the insurer will realize different revenue patterns over time. In addition, total premiums incurred by a borrower who prepays or defaults vary by the premium structure and the time of default/prepayment. The rationales for using different premium structures from either the borrowers' or the insurers' perspectives have not yet been studied in a rigorous manner.

Numerous mortgage default pricing articles have been published over the last two decades. Von Furstenberg (1969), Vandell (1978), Jackson and Kaseman (1980), and Swan (1982) study the value of mortgage default risk using econometric models. Campbell and Dietrich (1983) and Vandell and Thibodeau (1985) address the pricing of mortgage default risk and mortgage insurance with a utility maximization approach. Foster and Van Order (1984), Epperson, Kau, Keenan, and Muller (1985), and Cunningham and Hendershott (1984) use contingent claim pricing approaches to price mortgage default risk. Kau, Keenan, Muller, and Epperson (1992), study the value of default risk when prepayments and defaults are interrelated. Cunningham and Capone (1990), Ambrose and Capone (1996), and Deng and Calhoun (1997) focus their studies on the estimation of mortgage termination rates with historical data. Deng, Quigley and Van Order (1994) develop a conditional hazard model to estimate the default function.

Most of these papers focus on the valuation of default risk as a lump sum (upfront premium). However, literature that goes beyond the valuation of upfront premiums to study the effects of using different premium structures to cover default risk is almost nonexistent.

Mortgage insurance differs from other types of insurance in several respects. These differences make it difficult to adopt techniques developed elsewhere in the insurance industry. First, casualty insurance covers a single period, so the historical performance of a particular policy can be used in determining the premium to be charged in subsequent periods. This information cannot be used in determining mortgage insurance premiums, because mortgage insurance covers multiple periods, and the premium for the life of the mortgage is defined at the origination date. Second, in contrast to life insurance, mortgage insurance has a definite termination date and the claim risk decreases rather than increases over time due to the amortization schedule. Third, with proper geographic diversification, other types of insurers can usually reduce risk exposure to a minimum; however, because the prepayment and default rates of mortgages are highly dependent on macroeconomic variables such as interest rates, house price growth rates, and household income (or unemployment rates), substantial systematic risk is involved in mortgage insurance. …