本文使用先前文獻中被廣為應用於評價利率衍生性金融商品的HJM架構，輔以四種不同的隱含波動函數，對於歐式價平交換利率選擇權商品進行評價以及預測。由於波動率並非行恆常不變，因此本文採用了四種不同的波動函數結構，包含(1)常數型波動函數(ABS)、(2)與利率有方差關係之波動函數(SQR)、(3)指數遞減型波動函數(EXP)與(4)駝峰型波動函數(HUMP)。上述函數之因子個數決定於主成分分析的結果。藉由比較不同波動結構，進行模型間，樣本內評價誤差以及樣本外預測誤差的分析比較。實證結果顯示，HUMP模型無論在樣本內的評價誤差或是兩組樣本外預測誤差皆有最出色的表現，顯示具備捕捉駝峰型波動結構的波動函數之評價與預測績效皆勝過於無駝峰型波動結構的模型。EXP模型則在所有模型中表現次佳。雖然其波動函數未具備駝峰型態，然其捕捉駝峰型波動曲面的效果也相當出色。至於ABS模型以及SQR模型，其評價以及預測的表現皆不盡理想，顯示其捕捉駝峰型波動曲面的效果不明顯。 This study evaluates four one-factor implied volatility functions in the HJM class, with the use of swaps and at-the-money European swap options. The aim of this study is to observe the difference between these four models in in-sample pricing errors and out-of-sample prediction errors. The implied volatility functions applied in this study includes four models: (1) Constant volatility(ABS)、(2) Square-root volatility(SQR)、(3) Exponential decaying volatility(EXP), and(4) Hump-shaped Volatility(HUMP). By using of Principle Component Analysis, we are able to determine the number of factor that would affect implied volatility. The results indicate that the HUMP model outperforms other modes in both in-sample and out-of-sample pricing and predicting fit. This shows that model with humped displays a better pricing and predicting result than those without humped. The EXP model, which performs well in capturing the hump-shaped implied volatility surface, is the second-best model. Other models are inferior to the HUMP model and the EXP model in both cases.
