Estimation of Housing Price Jump Risks and Their Impact on the Valuation of Mortgage Insurance Contracts

TLDR

Housing price jump risk and the subprime crisis have heightened the need for precise mortgage insurance premium estimation. The study derives a mortgage‑insurance pricing formula by modeling housing prices with a jump‑diffusion process that captures abnormal shock events. The jump‑diffusion assumption is validated against U.S. monthly new‑home returns (1986‑2008) and the model examines how shock frequency, abnormal mean and volatility of jump size, and normal volatility affect premiums.

Abstract

Housing price jump risk and the subprime crisis have drawn more attention to the precise estimation of mortgage insurance premiums. This study derives the pricing formula for mortgage insurance premiums by assuming that the housing price process follows the jump diffusion process, capturing important characteristics of abnormal shock events. This assumption is consistent with the empirical observation of the U.S. monthly national average new home returns from 1986 to 2008. Furthermore, we investigate the impact of price jump risk on mortgage insurance premiums from shock frequency of the abnormal events, abnormal mean and volatility of jump size, and normal volatility. Empirical results indicate that the abnormal volatility of jump size has the most significant impact on mortgage insurance premiums.