臺灣博碩士論文加值系統

根據資產負債管理相關文獻可知，資產負債管理免疫策略的核心工具為資產與負債的平均存續期間與凸性，因此平均存續期間與凸性的衡量準確性將嚴重影響資產負債管理免疫策略的成效，而傳統的平均存續期間與凸性的衡量方式均未同時考量資產與負債的利率隨機性與附選擇權性質，這將使得傳統方式的衡量準確性受到嚴重的質疑。因此，本研究將以住宅抵押貸款為研究對象，探討適用於資產負債管理之貸款平均存續期間與凸性估計模型，並提出模型應符合三大主張，分別為利率為一隨機過程、現金流量為模型的內生變數，以及貸款存在提前清償狀況等，其中提前清償機率為利率的函數。
然而，過去相關研究，如Anderson, Barber, and Chang(1993)與Tzeng, Wang, and Soo(2000)所提出之模型皆尚未解決上述三大狀況。因此，本研究乃建構出一套模型，期能充分反應住宅抵押貸款負凸性的重要特質，並且有相對較低的估計誤差；此外，在資產負債管理應用方面，本模型亦具有估計誤差對資產負債管理免疫策略所造成的負面衝擊最小之特性。綜言之，在預期未來利率變化較大的情況下，以本模型進行資產負債管理免疫策略，應能獲得較好的免疫效果。

Literature working on the Asset/Liability Management (ALM) appeared that the duration and convexity of asset and liability is the core of surplus management. Therefore, the accuracy on the measurement of duration and convexity will have an impact on the results of surplus management. Because of the classical measurement of duration and convexity does not involve the interest rate stochastic process and the embedded option properties, it will procure a strong mistrust on accuracy. Therefore, this paper that devised the estimation model of residential mortgage’s duration and convexity for surplus management argued that the estimation model should conform three assumptions: interest rate follows the stochastic process, cash flow is the endogenous variable of model and loans exist prepayment. Moreover, prepayment rate is the function of interest rate.
Previous studies on duration model don’t conform the above-mentioned three assumptions, such as Anderson, Barber, and Chang (1993) and Tzeng, Wang, and Soo (2000). Hence, this paper established a model, which could response the negative-convexity properties of residential mortgage loans adequately, and appeared relatively lower estimation error. In additional, the estimation error of this model results in the lowest negative influence for surplus management rather than others. In conclusion, under the expectation that the interest rate would have greater change in the future, this model should acquire better immunization result for the immunization strategy of surplus management.

摘 要 I
英文摘要 II
誌 謝 III
目　錄 IV
表目錄 VI
圖目錄 VII

第壹章　緒論 1
第一節　研究動機與目的 1
第二節　研究方法 3
第三節　研究範圍與限制 3
第四節　研究流程與內容 4
第貳章　文獻探討 6
第一節　資產負債管理免疫策略 6
第二節　傳統平均存續期間與凸性 9
第三節　抵押貸款平均存續期間與凸性 15
第四節　隨機利率平均存續期間與凸性 18
第五節　提前清償機率模型文獻回顧 24
第參章　模型推導 33
第一節　模型基本架構 33
第二節　隨機利率模型 35
第三節　現金流量估計模型 37
第四節　提前清償機率模型 42
第五節　平均存續期間與凸性估計模型 50
第肆章　模擬分析 53
第一節　基本模擬參數設定 53
第二節　模擬結果分析 59
第三節　敏感性分析 63
第四節　模型比較分析 74
第五節　模型估計誤差對資產負債管理的衝擊80
第伍章　結論與建議 86
第一節　研究結論 86
第二節　後續研究建議 90
參考文獻 91
附錄 99

表3.1　模型外部環境參數符號表52
表3.2　模型合約內容參數符號表52
表4.1　合約內容參數基本設定表54
表4.2　VASICEK隨機利率模型參數估計結果55
表4.3　貸款利率相對於指標利率的波動性比率估計結果56
表4.4　提前清償機率模型LOGIT迴歸係數設定表58
表4.5　平均攤還本息型住宅抵押貸款模擬估計結果59
表4.6　到期還本型住宅抵押貸款模擬估計結果60
表4.7　比較模型定義關係表76
表4.8　模型估計誤差對淨值殘餘變動率的影響-平均攤還型貸款83
表4.9　模型估計誤差對淨值殘餘變動率的影響-到期還本型貸款84
表5.1　模型參數與估計結果關係表89

圖1.1　研究流程圖5
圖4.1　銀行隔夜拆款利率走勢圖54
圖4.2　購屋貸款利率與隔夜拆款利率走勢圖55
圖4.3　未調整係數前之平均攤還本息型提前清償機率57
圖4.4　到期還本型提前清償機率57
圖4.5　調整係數後之平均攤還本息型提前清償機率58
圖4.6　平均攤還本息型住宅抵押貸款模擬結果59
圖4.7　到期還本型住宅抵押貸款模擬結果60
圖4.8　平均攤還本息型住宅抵押貸款提前清償機率模擬結果61
圖4.9　到期還本型住宅抵押貸款提前清償機率模擬結果62
圖4.10　住宅抵押貸款的價格行為62
圖4.11　每次調整利率上下限與模型估計結果之關係64
圖4.12　利率最高上限與模型估計結果之關係65
圖4.13　每次調整利率的天數與模型估計結果之關係66
圖4.14　每次付款的天數與模型估計結果之關係66
圖4.15　貸款成數與模型估計結果之關係67
圖4.16　貸款年限與模型估計結果之關係68
圖4.17　原始合約利率與平均存續期間估計結果之關係70
圖4.18　原始合約利率與凸性估計結果之關係70
圖4.19　貸款利率相對波動性與平均存續期間估計結果之關係72
圖4.20　貸款利率相對波動性與凸性估計結果之關係72
圖4.21　指標利率起始值與模型估計結果之關係73
圖4.22　各種比較模型之平均存續期間估計結果76
圖4.23　各種比較模型之凸性估計結果77
圖4.24　各種平均存續期間估計模型之MSE79
圖4.25　各種凸性估計模型之MSE79

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