不動產抵押貸款是銀行主要的業務來源,隨著ECFA的生效,銀行有了向外發展的契機,不動產抵押貸款的承做量也會增加。隨著景氣復甦,房價不斷的飆升,但利率卻仍處於低點,根據這兩種情況,本文想探討:1、在「短期」下,假設房價無限大時,利率與時間變化對抵押貸款價值的影響? 2、在「短期」下,假設利率有短暫的僵固性時,房價與時間變化對抵押貸款價值的影響,以及這兩種情況所可能得到的風險溢酬為何? 故本文利用Crank-Nicholson的有限差分法 (Crank & Nicholson, 1947),配合利用隨機過程推導出的偏微分方程來模擬出結果。結果發現,利率提高、房價提高、貸款年限增加都會對銀行帶來風險,所以銀行亦會對此要求較高的風險溢酬。
The Bank business of main sources is real estate mortgage, with the effect of ECFA, the bank will have opportunities developed outward, real estate mortgage will increase. With the economic recovery, house prices continue to soar, but still at a low interest rate, according to both cases, this article would like to explore: First, in the "short term", we assuming house price is infinite, the interest rates on mortgages with time the impact of mortgage value? Second, in the "short term", we assumed short-term interest rate rigidity, the house price and time impact on the value of mortgage, and the risk premium in both cases. Therefore, this paper use Crank-Nicholson finite difference method (Crank & Nicholson, 1947), and stochastic processes to simulate the results. The results showed that higher interest rates, house prices increase, the loan period increase would risks for banks, so banks will have higher risk premium.