狀態相依利率模型 －結合GARCH（1,1）與變異性參數模型

Abstract

摘 要 發展至今，利率模型主要可分為均衡模型和無套利模型兩大類。本研究係以均衡模型的理論為基礎，採Vasicek 和CIR 利率模型之架構，藉由狀態變數之引進，考慮到權益市場和債券市場之風險前瞻性資訊對利率波動結構的影響。亦即使本研究所提出之「狀態相依利率模型」中的參數，可隨時間變動，以反映市場未來的變化。估計參數的方法，則是透過GARCH(1,1)模型以降低利率之異質變異，改善預測效力。最後，利用狀態相依利率模型模擬出在實際測度下之利率期間結構，做為「標的資產不可連續交易」的商品評價之基礎。 故本研究主要目的在於： 一、 與Vasicek 模型（固定參數）之預測結果相比，以驗證本研究提出之「狀態相依利率模型」，的確有提升對利率期間結構之預測效力。 二、 驗證狀態相依利率模型在配適不同形狀之利率期間結構時，例如：上升下降和平坦三種型式，是否皆能較固定參數Vasicek 模型有更好的預測能力。 三、 以蒙地卡羅法，模擬出實際測度下之利率期間結構，並將其應用於「標的物不可連續交易之衍生性商品」評價上。 本研究之結論為： 一、 本研究所提之「狀態相依利率模型」，在不同的樣本期間下，其預測結果皆較固定參數Vasicek模型更為貼近實際之利率期間結構。 二、 狀態相依利率模型分別預測平坦、上升和下降之利率期間結構時，其預測準確度，都較原本之固定參數Vasicek模型來的高。 三、 本研究所提出之「狀態相依利率模型」順利藉由變異性參數模型，引入真實世界中，外生前瞻性資訊對利率結構波動之影響。並可輔以蒙地卡羅法，模擬出在real measure下之利率期間結構，提供未來各式「標的物不可連續交易」之衍生性商品評價上（例如：房貸基礎證券）。

Abstract The interest rate model could be divided into two categories: equilibrium models and no-arbitrage models. The foundation of this paper is the theory of equilibrium model. The state-dependent variables are introduced to both the Vasicek model and the CIR model. The interest rate fluctuations influenced by the foresighted information of the equity and bond market are also taken into consideration. Coefficients of the state-dependent interest rate model vary with time and reflect the future changes in the market. In reducing the heteroscedasticity of interest rates, GARCH(1,1) is used for coefficients estimating and expected to improve the model forecasting potency on yield curves. Finally, we use the state-dependent interest model to simulate the term structure under real measure which can be used on pricing the product of non-traded target asset. The main objectives of our research are as follows: (1)Verify the improvement of the forecasting potency of the state-dependent interest rate model by comparing it to original Vasicek model. (2)Make certain the superior forecasting abilities of sate-dependent interest rate model by different simulated yield curves. (3)Pricing the product of non-traded target asset by Monte Carlo simulated term structures The empirical result shows the term structure produced by state-dependent interest rate model are better than simulated by the Vasicek model. In different shape of simulated term structures, the state-dependent interest model always exhibits lower prediction errors in contrast to the Vasicek model. We successfully introduce state variables to the equilibrium model. Indeed, the state-dependent interest rate model with varying coefficients improves the capibility of forecasting.