The valuation and analysis of mortgage insurances with the cyclical property of housing prices

[[abstract]]This research rst re nes the pricing formula for mortgage insurance (MI) con- tracts proposed in Bardhan, Karapand za, and Uro sevi c (2006) based on a modi ed contract whose setting is closer to reality. Since housing prices are usually observed to be cyclic in the mean growth rate and volatility due to economic uctuations, our research further extends this modi ed MI pricing formula by taking into con- sideration the state-dependent property behind housing prices. Empirical analysis shows that the fair premium estimated with the state-dependent property for the U.S. market is higher than that when ignoring this property at the end of 2010. It indicates that incorporating the cyclical property in valuing MI contracts may facilitate to lessen the losses for mortgage insurers in the U.S. market, in which these companies operated at a loss during this period. By comparing the market premiums and fair premiums calculated from the proposed model, we nd evidence that the high-risk MI insured is largely subsidized by the low-risk insured in the U.S. market