Pricing mortgage insurance: Integrating target prescribed capital requirement for systematic risk

This study derives a closed-form formula for mortgage insurance (MI) premiums that accounts for systematic and idiosyncratic risks using option-pricing theory. This formula can be used to calculate the MI premium that incorporates the target prescribed capital requirement (PCR), which aims to manage systematic risk at a given confidence level. We illustrate the application of the model using U.S. state-level housing market data from 1991Q1 to 2017Q2, with 105 observations per state. Our results show that idiosyncratic risk exceeds systematic risk in the housing market. MI premiums, considering the target PCR, are larger than those without considering it. Sensitivity analyses further indicate that the MI premium increases with the parameters of both systematic and idiosyncratic risks. Our model and results should provide MI insurers with a practical tool for determining a fair MI premium under changing economic conditions and for strengthening risk management.