The Study on Estimation Model of Residential Mortgage Loans Duration and Convexity for Surplus Management

[[abstract]]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。[[abstract]]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