隨著金融市場的開放，越來越多的金融商品被開發出來以迎合市場參予者的需求，利率衍生性金融商品是一種以利率為標的的一種新金融商品，而這種新金融商品的交易量也是相當的可觀。我們在設計金融商品的第一步就是要去定價，在現實社會中利率是隨機波動的而不是像在B-S的選擇權公式中是固定的。隨機利率模型的用途就是在描述利率隨機波動的行為，進而對利率衍生性金融商品定價。本文嘗試以隨機利率模型估計台灣公債市場的殖利率曲線，而殖利率曲線的建立對於固定收益證券及其衍生性金融商品的定價是很重要的。在台灣大部分的利率模型的研究都是利用模擬的方式做比較，這也許是因為資料取得上的問題，本文利用CKLS(1992)所提出的方式以GMM(Generalized Method of Moment)的估計方法，利用隨機利率模型估計出台灣公債市場的殖利率曲線。本文中將三種隨機利率模型做比較他們分別為: Vasicek model (Vasicek 1977),、隨機均數的Vasicek 模型 (BDFS 1998) ，以及隨機均數與隨機波動度的Vasicek 模型 (Chen,Lin 1996). 後面兩個模型是首次出現在台灣的研究文獻中。在本文的附錄中將提出如何利用偏微分方程式(PDE)的方法求解出這三個模型的零息債券價格的封閉解(Closed-Form Solution)。文中利用台灣商業本票的價格當作零息債券價格的近似值，再以RMSE (Root mean squared Price Prediction Error)作為利率模型配適公債市場價格能力的指標。本文的主要貢獻在於嘗試以隨機利率模型估計出台灣公債市場的殖利率曲線，以及介紹了兩種首次在台灣研究文獻出現的利率模型，並且詳細推導其債券價格的封閉解，這對於想要建構一個新的隨機利率模型的研究人員而言，這是一個相當好的一個練習。

With the growth in the area of financial engineering, more and more financial products are designed to meet demands of the market participants. Interest rate derivatives are those instruments whose values depend on interest rate changes. These derivatives form a huge market worth several trillions of dollars.

The first step to design or develop a new financial product is pricing. In the real world interest rate is not a constant as in the B-S option instead it changes over time. Stochastic interest rate models are used for capturing the volatile behavior of interest rate and valuing interest rate derivatives. Appropriate models are necessary to value these instruments. Here we want to use stochastic interest rate models to construct the yield curve of Taiwan Government Bond (TGB) market. It is important to construct yield curve for pricing some financial instruments such as interest rate derivatives and fixed income securities.

　In Taiwan Although most of the research surrounding interest rate models is intended towards studying their usefulness in valuing and hedging complex interest rate derivatives by simulation. But just a few papers focus on empirical study. Maybe this is due to the problems for data collection. In this paper we want to use stochastic interest models to construct the yield curve of Taiwan’s Government Bond market. The estimation method that we use in this paper is GMM (Generalized Method of Moment) followed CKLS (1992).

I introduce three different interest rate model, Vasicek model (Vasicek 1977), Vasicek with stochastic mean model (BDFS 1998) and Vasicek with stochastic mean and stochastic volatility model (Chen,Lin 1996). The last two models first appear in Taiwan’s research. In the Chapter 3, I will introduce these models in detail and in the appendix of my thesis I will show how to use PDE approach to derive each model’s zero coupon bond price close-form solution. In this paper we regard Taiwan CP (cmmercial Paper) rates as a proxy of short rate to estimate the parameters of each model. Finally we use these models to construct the yield curve of Taiwan Government Bonds market and to tell which model has the best fitting bond prices performance. Our metric of performance for these models is RMSE (Root mean squared Price Prediction Error). The main contribution of this study is to construct the yield curve of TGB market and it is useful to price derivatives and fixed income securities and I introduce two stochastic interest rates models, which first appear in Taiwan’s research. I also show how to solve the PDE for a bond price and it is a useful practice for someone who wants to construct his/her own model.

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