This study advances the mortgage insurance pricing literature by providing theory and methods for incorporating both equity and ability-to-pay theories (Jackson and Kasserman, 1980). We develop a new option-based model by adding the current loan-to-value and debt service ratios to the pricing process of mortgage insurance (MI). Specifically, the MI is regarded as a portfolio of a series of put options to obtain the analytical pricing formulas. Under the consistent pricing framework, we also derive three types of MI contracts designed for different purposes: full MI can compensate mortgage lenders for default loss; maximum claim policies provide insurers with a limit loss; and partial indemnity policies can be adjusted to different insurance coverage for borrowers’ default losses. Finally, we conduct numerical and empirical analyses to evaluate how different designs of MI relate to insurance premiums, and to examine how housing price dynamics and income flow affect insurance premiums.

Great volatility in housing prices and the recent subprime crisis have drawn more attention to the default cost of mortgages for banks and insurance companies. Among contracts-related mortgage, mortgage insurance (MI) protects residential mortgage lenders (often banks) against losses arising from borrowers’ defaulting on mortgage loans. It provides a reliable instrument for transferring credit risks from banks to mortgage insurers or the capital market. In the US and other developed countries, a robust MI scheme plays an important role in the functioning of the housing finance market since it reduces the risk exposure of lenders and promotes the creation of secondary mortgage markets (Canner et al., 1994). Both Fannie Mae and Freddie Mac, government-sponsored agencies of the US, require home buyers whose loan-to-value ratio of mortgages is 80% or more to get insurance. Many MI policies are also procured specifically to protect investors in mortgage-based securities so that the investor receives the insurance proceeds if borrowers default. MI in the US is provided by two government agencies—Federal Housing Administration and the Department of Veterans Affairs, as well as by private mortgage insurers. The demand for similar risk-sharing mechanisms exists in the emerging markets as well (Bardhan et al., 2006).

The primary contributions of this paper are as follows: First, both CLTVR and CDSR are regarded as the two main factors of borrowers’ credit quality: (1) They are embedded into the MI pricing process. This approach improves the assumption of the exogenous default probability in the option-based methods for assessing MI; and (2) some contracts are designed to provide the borrowers an option for insurance coverage, and to help the insurers avoid moral hazard risks. These improvements promote MI contracts as more practicable and applicable than those in previous literature.

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