資本寬容對房屋抵押貸款保險之影響

The Impact of Capital Forbearance on Mortgage Insurance

房屋抵押貸款保險制度在國外已經行之有年，並成為房貸市場重要機制。但是，在次貸風暴期間，大型房貸保險公司無不承擔龐大損失，各國政府卻不敢貿然讓房貸保險公司倒閉，以免造成系統性的金融危機。有鑑於此，本研究除了考慮房貸保險公司違約風險，並同時考量資本寬容機制，推導出房屋抵押貸款保險契約之公平保費公式解。藉由數值分析可知，資本寬容程度越高，房貸保險契約之保費越高。此外，隨著資產負債價值比例增加，資本寬容門檻值對於房貸保險保費之影響更顯重要。最後，藉由延長房貸保險公司經營時間來解決房貸保險公司資本不足問題，亦將使得房貸保險契約之保費上升，且當資產負債價值比例增加，延長經營時間效果對保費上升之效果亦趨明顯。

The system of mortgage insurance has developed over a long period of time and plays an important role in the housing financial market. Since many mortgage insurers suffered huge losses during the subprime mortgage crisis which resulted in capital scarcity, the government came under great pressure to bail them out in order to avoid a systemic economic crisis. Hence, this paper derives a closed-form formula for a mortgage insurance contract that takes into consideration counterparty default risk and capital forbearance. From the numerical analysis, we demonstrate that the mortgage insurance premium is an increasing function of the forbearance threshold. Furthermore, a higher asset-liability ratio leads to a more significant impact of the forbearance threshold on the fair premium for mortgage insurance. In addition, the longer the capital forbearance period and the higher the asset-liability ratio, the higher the fair premium of mortgage insurance.