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.

Amin, K., and Morton, A. (1994), “Implied Volatility Functions in Arbitrage Free Term Structure Models,” Journal of Financial Economics, 35, 141-180.
Bühler, W., Uhrig-Homburg, M., Walter, U., Weber, T. (1999), “An Empirical Comparison of Forward-Rate and Spot-Rate Models for Valuing Interest-Rate Options,” Journal of Finance, 54, 269-305.
Björk, T. (1998), Arbitrage Theory in Continuous Time, Oxford University Press.
Black, F. (1976), “The Pricing of Commodity Contracts,” Journal of Financial Economics, 3, 167-179.
Brace, A., Dun, T., and Barton, G. (1998), “Towards a Central Interest Rate Model,” FMMA notes working paper.
Brace, A., Gatarek D., Musiela, M. (1997), “The Market Model of Interest Rate Dynamics,” Mathematical Finance, 7, 127-155.
Brigo and Mercurio (2001), Interest Rate Models － Theory and Practice, Springer.
Chen, Ren-Raw and Louis O. Scott (1993), “Maximum Likelihood Estimation for a Multifactor Equilibrium Model of the Term Structure of Interest Rates,” Journal of Fixed Income, 3, 14-31.
De Jong, F., Driessen, J., and Pelsser, A. (1999), “LIBOR and Swap Market Models for the Pricing of Interest Rate Derivatives: An Empirical Analysis,” Preprint.
Driessen, J., P. Klaassen, and B. Melenberg (2003), “The Performance of Multi-Factor Term Structure Models for Pricing and Hedging Caps and Swaptions,” Journal of Financial and Quantitative Analysis, 38, 635-672.
Fan, R., A. Gupta, and P. Ritchken (2001), “On Pricing and Hedging in the Swaption Market: How Many Factors, Really?”, working paper, Case Western Reserve University.
Gupta, A., and M. Subrahmanyam (2001), “An Examination of the Static and Dynamic Performance of Interest Rate Option Pricing Models in the Dollar Cap-Floor Markets,” working paper, New York University.
Hull, John C. (2003), Option, Futures, and Other Derivatives, 5th ed., Upper Saddle River, New Jersey: Prentice-Hall.
Jagannathan, R., A. Kaplin, and S. Sun (2001), “An Evaluation of Multi-Factor CIR Models Using LIBOR, Swap Rates, and Cap and Swaption Prices,” working paper, Northwestern University.
Jamshidian, F. (1997), “LIBOR and Swap Market Models and Measures,” Finance and Stochastics, 1, 293-330.
Jäckel , Peter (2002), Monte-Carlo Methods in Finance, John Wiley & Sons.
Jegadeesh N., and G. Pennacchi (1996), “The Behavior of Interest Rates Implied by the Term Structure of Eurodollar Futures,” Journal of Money, Credit, and Banking, 28, 426-446.
Longstaff, F., P. Santa-Clara, and E. Schwartz (2001), “The Relative Valuation of Caps and Swaptions: Theory and Empirical Evidence,” Journal of Finance, 56, 2067-2109.
Miltersen, K.R., Sandmann K., Sondermann D. (1997), “Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates,” Journal of Finance, 52, 409-430.
Musiela, M., and Rutkowski, M. (1997), “Continuous-Time Term Structure Models: Forward Measure Approach,” Finance and Stochastics, 4, 261-292.
Pelsser, A. (2000), Efficient Methods for Valuing Interest Rate Derivatives, Springer, Heidelberg.
Peterson, S., R. Stapleton, and M. Subrahmanyam (2001), “The Valuation of Caps, Floors and Swaptions in a Multi-Factor Spot-Rate Model,” working paper, Stern School of Business, New York University.
Rebonato, R. (1999), “On the Simultaneous Calibration of Multifactor Lognormal Interest Rate Models to Black Volatilities and to the Correlation Matrix,” Journal of Computational Finance, 4, 5-27.
Riccardo Rebonato (2002), Modern Pricing of Interest-Rate Derivatives － The LIBOR Market Model and Beyond, Princeton University Press.