A Comparison of Prepayment Rates among Pools of Home Equity Loans: An Exponential Regression Approach

[[abstract]]提前清償動態為利率與現金流量分割等決策所需之關鍵資訊，Schwartz(1989)與Hall(2000)等文獻是以特定連續分配為提前清償危機函數基線。然而，實際清償率是群組本金提前還款的離散時間條件機率，按特定函數很難適切捕捉其動態。本文以1,246戶浮動利率，固定金額本息攤還之房屋修繕貸款為樣本，計算個別貸款分期提前還款金額，假設合計金額為群組該期的平均數，再逐期比較差異，依有無顯著差異與重要性原則合併期數，建立分段指數迴歸模式的提前清償率估計值與信賴區間。 以群組年紀為單變數的提前清償函數，隨年齡增加呈現遞增後驟降再走平，最後快速上升的型態，其中10.5歲至12.5歲有清償疲乏現象。此外，本研究以貸款年紀與餘額分群，估計不同群組的重新融資意願、非住宅投資報酬與風險承受程度等對提前清償的影響。結果顯示：利差比、股票指數報酬與波動性對中年紀與高餘額群組的清償率有顯著正相關。利差比有高度路徑相依的關係，而中高年紀與高餘額群組的風險承受能力於5年期間由高變低。[[abstract]]A prepayment rate is recognized as the prepaid proportion of the remaining principal in each pool of loans. The behavior of prepayment rates is a key component of determining an interest level and stripping a mortgaged-back cash flow. In this article we propose a piecewise exponential regression model for the prepayments at discrete intervals. The data set contains 1,246 close-end and adjustable-rate home equity loans. For each pool of loans, the prepaid principal of each loan is summed at each interval. The prepayments for several intervals are collapsed as one prepayment when the interval estimates are evaluated. We investigate the burnout effect and the effects of the explanatory variables on the prepayment rates, which are the conditional probabilities of prepayments at each interval. The explanatory variables include age, loan amount, refinancing incentive, and non-housing investment and risk tendency. In the burnout effect, we find that the prepayments are associated with age. They peak at about seven and half years, decline rapidly thereafter and stay stable between ten and half years and twelve and half years. In the effects of the explanatory variables, we find that (a) the ratio of the spread between the weighted average mortgage rate (i.e., WAC) and one-year deposit rate to one-year deposit rate, the return and fluctuation of stock index are positively correlated with prepayments, (b) the ratio of the spread to one-year deposit rate is path-dependent when prepayments are estimated, (c) in each pool of moderate age and old age, as well as in the pool of high outstanding amount, their capability of risk-taking of three years is greater than that of five years