CIR變異性參數利率模型－信用卡債權證券評價之應用

吳紫揚(Tzu-Yang Wu)

指導教授 ： 廖咸興 ； 葉小蓁

國立臺灣大學/管理學院/財務金融學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.10052

摘要

本文將CIR利率模型與系統變異性參數模型結合，創造出CIR變異性參數利率模型，使得在殖利率曲線未知的狀況下，利率隨機過程能夠反應總體經濟情況變化所造成之影響。將CIR變異性參數利率模型中變動參數 的變動情形，當成是與影響利率的總體經濟變數－匯率（NT/USD）與CPI月增率－有關，藉由未來每一期匯率月增率與CPI月增率的變動解釋 的變動。

由於利率模型的參數正確與否，將會直接地影響模型的準確性，因此參數估計便顯得十分重要，選用的參數必須盡量接近實際市場資料。為了解決短期利率具有異質變異現象的問題，最後選擇利用AR(1)搭配GARCH模型建立適合台灣市場的短期利率模型，利用實際市場資料估計CIR利率模型與CIR變異性參數利率模型的參數，藉此盡可能地模擬實際的利率變動。

此外，並以信用卡債權證券為例，比較CIR利率模型與CIR變異性參數利率模型在蒙地卡羅模擬法下之模擬價格差異性。研究結果顯示，兩種定價模型所得到的價格差異性不大。由於國內在資產證券化領域之相關論文中，尚未提出有關信用卡債權證券之評價文獻，故本文為第一篇針對信用卡債權證券的評價方法作詳細探討之論文。因此本文之次要目的在於提供適合評價台灣市場信用卡債權證券的定價模型。

最後進行敏感性分析所得到之結論如下：
1. 其他條件不變下，若短期利率長期水準 愈大，則信用卡債權證 券價格愈低。
2. 其他條件不變下，若調整速度ｋ愈大，則信用卡債權證券價格愈高。
3. 當調整速度ｋ的變動或是短期利率的長期水準 的變動時，對還本方式為控制累積還本法的信用卡債權證券之價格影響會比較大。

關鍵字

CIR利率模型 ； GARCH模型 ； 信用卡債權證券 ； 變異性參數模型

並列摘要

This paper combines the CIR model and varying coefficient model to create a CIR varying coefficient model. Under this model, interest rate stochastic process can reflects the effect of micro-economy changes while term structure is unknown. Let exchange rate (NT/USD) and inflation rate (monthly increasing rate of CPI) explain the variation of the varying coefficient .

The accuracy of the interest rate model will be influenced by the selected coefficients, so it’s important to choose suitable coefficients closing to the real market. In order to explain the heteroskedasticity of short rate, we adopt AR(1) accompanied with GARCH model to estimate the coefficients of CIR and CIR varying coefficient model, and then simulate the changes of interest rate.

What’s more, we take Credit Card ABS for example and use Monte Carlo Simulation Method to calculate their theoretical price under each of the two different interest rate models. The result shows that price difference is not significant.

The results of sensitivity analyses are as fellows：
1. Others being equal, when reversion level is larger, the price will be lower.
2. Others being equal, when reversion rate ｋ is larger, the price will be higher, too.
3. When reversion rateｋ or reversion level change, the price of Credit Card ABS will change more significantly under controlled accumulation than controlled amortization.

並列關鍵字

CIR Model ； Varying Coefficient Model ； GARCH Model

參考文獻

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