從浮動利率貸款論利率風險與信用風險之互動關係

Abstract

我們使用樹狀結構描述利率與房價，並且利用貸款成數(LTV)以及支付金額對收入比率(PTI)來做違約條件的設定，進而計算出違約機率。接著利用敏感性分析測試各參數對違約機率的影響，包含起始利率、利率均數回歸之速度、利率變異數、服務現金流量、房價變異數以及利率與房價間的相關係數。 最後得出以下結論： (1)在其他條件不變下，浮動利率貸款之違約機率較固定利率貸款之違約機率大。 (2)起始利率、利率變異數、服務現金流量以及房價變異數與違約機率呈現正相關情形。 (3)利率均數回歸之速度以及利率與房價間的相關係數與違約機率呈現負相關情形。

The article uses a bivariate pricing lattice to observe different interest rates and housing prices. Then we use loan-to-value ratio and payment-to-income ratio to set the default conditions. And the probabilities of default are then calculated. We have sensitivity tests that describe the changes of the probabilities of default due to the changes of different variables including initial interest rate, mean-reverting speed, volatility of interest rate, cash service flow, volatility of house price and correlation coefficient between interest rate and housing price. The conclusions are as follows: (1)Under the same condition except that interest rate settings are different, the probabilities of default of adjustable rate mortgages are higher than which of fixed rate mortgages. (2)Initial interest rate, volatility of interest rate, cash service flow and volatility of housing prices appear to be positively related to the probabilities of default. (3)Mean reverting speed of interest rate and correlation coefficient between interest rate and housing price appear to be negatively related to the probabilities of default.