Valuing Vulnerable Mortgage Insurance Under Capital Forbearance

Abstract

This study sets up a contingent-claim framework incorporating the default risk of a mortgage insurer and the capital forbearance of regulators to value mortgage insurance (MI) contracts. We further investigate how critical policy parameters, such as capital requirements, prompt closure, and time of delay, relate to the MI premium by deriving a closed-form solution and evaluating its partial derivatives. The solutions show a negative cross effect of forbearance threshold and time delay on MI, indicating that a lower forbearance threshold and a longer period of time delay both expand their positive impacts on the price of MI. The numerical results show that an insurer's default risk premium can be substantial in the presence of a catastrophic risk in the housing price. For mortgage insurers with a lower asset-liability ratio, the effect of the interest rate risk on the MI premium is more obvious and noteworthy. Moreover, the forbearance threshold effect and capital requirements effect are more significant than the time delay effect on the MI premium.