模糊迴歸與利率期限結構估計

本文以Vasicek and Fong (1982)所提出的分段三次方指數樣條函數與修正之McCulloch (1975)指數多項式函數，來建構台灣公債市場之利率期限結構，並同時比較前述模型在配適能力的優劣。實證結果發現，分段三次方指數樣條函數不論在模型之精確度與平滑度方面，均優於修正之指數多項式函數。此外，為使估計之利率期限結構模型能充分反映市場所呈現的資訊，本文進一步運用De Andrés and Ternceño (2003)提出之模糊迴歸法，針對配適能力較佳之分段三次方指數樣條函數模型進行模糊化操作。此方法最大優點在於能對利率之不確定性加以量化，以建構利率期限結構的區間範圍，進而反映市場參與者對於未來利率走勢的預期。綜而言之，相較於傳統利率期限結構估計模型，模糊迴歸法能提供較佳的彈性於處理利率不確定性的問題。

關鍵字

分段三次方指數樣條函數；指數多項式函數；利率期限結構；模糊迴歸法

並列摘要

This paper employs the piece-wise exponential spline function defined by Vasicek and Fong (1982), and the modified exponential polynomial function originally proposed by McCulloch (1975) to fit the term structure of interest rates in Taiwan Government bond market. The empirical results indicate that the piece-wise exponential spline function has better fitting performance in both accuracy and smoothness. In addition, to sufficiently reflect all information in bond market, this paper uses the fuzzy regression methods proposed by De Andrés and Ternceño (2003) to fuzzify the term structure of interest rates estimated by the piece-wise exponential spline function described above. The main advantage of this approach is that it enables to quantify the interest rates uncertainty and to set a range of term structure movements. Thus, it can help to reflect the anticipation of future interest rates trend for all market participator. Comparing with traditional term structure fitting models, it could provide a more flexible way to deal with the interest rates uncertainty.