本篇論文中，結論顯示在波動性為時間齊次或是常態的假設下，以三因子模型去評價利率上限，其定價較為精準，但是以單因子及二因子模型來評價，則表現普遍不佳;若是以三因子模型去評價交換選擇權，在選擇權到期年限為兩年或是三年的情況下，其定價比單因子及二因子模型精準，但是在選擇權到期年限為七年的情況下，並不保證三因子模型定價比單因子及二因子模型精準。此外也發現市場模型中的波動性參數如果採用時間齊次性假設，則定價表現較佳。這是個很重要的結果，因為在文獻上，大部分的學者總是採用Rebonato (1998)所建議的參數化波動性假設來評價利率衍生性商品，然而本文卻發現此種假設的定價表現不佳。 In this paper, we find that for caps, when we assume volatilities are time-homogeneous or flat, 3-factor model is better than 1- and 2-factor model. For swaptions, no matter how many years expiration is, if the tenor is shorter (2 or 3 year), the pricing performance in the 3-factor mode is better than others. But if the tenor is longer (7 year), the pricing performance of the 3-factor model is not guaranteed to be better than that of other models. If we use time-homogeneous volatilities to evaluate caps or swaptions, pricing performance is very well in most situations. We have to notice this result. Because in the literatures, most of researchers always use parametric instantaneous volatilities (case 3) that are suggested by Rebonato (1998) to evaluate interest rate derivatives. However, we show in this paper that the pricing performance under a parametric instantaneous volatilities assumption might be not very satisfactory.
