縮減式信用風險模型之研究

Abstract

近幾十年來，評估信用風險的文獻發展非常迅速。以模型的方法來說，可粗分為兩大領域：結構式模型和縮減式模型。本論文主要以縮減式模型為基礎，包含了結構式模型具有經濟直覺的優點，去建構兩個信用風險評估模型Jarrow04 模型和Jarrow09模型。利用債券的無套利定價準則，我們可以推導零息債券的定價公式。本研究以美國兩大企業所發行的零息債券為研究對象，透過市場所觀察到的公司資訊，對兩零息債券進行評價。此模型可以模擬許多條變數路徑，並得出變數的分配。有了變數的分配與零息債券的定價公式，我們可以推估出未來各期的債券價格。文章最後藉由預測誤差值來比較兩模型評價的準確性。本研究發現，長期債券處於金融危機時，Jarrow04模型因考慮了債券發行者的現金餘額，因此有較佳之預測能力；非金融危機時期，則適用Jarrow09模型。至於性用良好的短期債券，因為其接近於無風險債券，利用兩模型之預測差異性不大，因此建議選用Jarrow09 模型來模擬零息債券的價格，較為省時。

In the recent decades, literatures on credit risk measurement evolved dramatically. According to modeling techniques, they can be roughly grouped into two major categories, “structural models” and “reduced form models.” This thesis is based mainly on reduced form models and connects with structural models which include the advantages of the economic intuition to set up two models of evaluating credit risk, Jarrow04 Model and Jarrow09 Model. With the criteria of no-arbitrage pricing of bonds, pricing formulae of the two proposed reduced form models are derived for zero-coupon bonds. This research takes samples from zero-coupon bonds issued by the two major U.S. enterprises. Under the company’s information observed by market, evaluate the two zero-coupon bonds. The models can simulate many random variable paths and then the distributions of random variable. With variable distribution and the pricing formulae of zero-coupon bonds, we can obtain the bond prices in future periods. Furthermore, forecast errors are showed to compare the accuracy of valuing in the two models. We find that Jarrow04 Model has the best prediction ability for long-term zero-coupon bond during the financial crisis, and Jarrow09 Model predicts better for long-term zero-coupon bond not in financial crisis. In addition, for short-term bond, since it is close to risk-free bonds, there is no difference between the two models. Therefore, we suggest that using Jarrow09 Model to valuate zero-coupon bond is more convenient.