評估信用風險之可轉換公司債評價模型：結構式模型

Abstract

近年來討論convertible bond pricing的論文如Hung & Wang(2002)和Chamber & Lu(2007)，都使用樹狀結構模擬股價和短利的變化，而信用風險計算都是參照Jarrow and Turnbull (1995)提出的縮減式模型(Reduced model)，股價高低並不影響公司違約機率。本研究考慮股價對違約機率的影響，以結構式信用風險模型(Structural Model)與首次通過模型(First passage time model)評價違約機率，當股價越高，公司資產相對越高，而違約機率應該越低，使評價模型更貼近市場真實狀況。 本研究先探討股價變動、利率為常數的一因子模型，透過股價樹(CRR Tree)來模擬股價變動，建構可轉債評價模型之樹狀結構，透過倒推法(Backward Induction)，求出可轉債期初價格；再討論股價變動、利率變動的二因子模型， 透過利率樹(Hull-White Tree)來模擬利率變動，並將股價樹與利率樹結合成可轉債評價模型之樹狀結構，透過倒推法，求出可轉債期初價格。此外，本研究參考Brenen & Schwartz (1980)提出的可轉換公司債評價模型，當債券持有人決定將手中可轉債轉換成股票後，因股權稀釋，股價應該向下做微幅修正，可轉換公司債價格也會隨之下降，使評價更精確。

Recently, many convertible bond pricing papers, like Hung and Wang(2002) and Chamber and Lu(2007), use the tree structure to modeled the evolution of stock price and the short rate. The default risk is model by Jarrow and Turnbull (1995) default intensity model and the stock price process is irrelevant to the default probability. Indeed, the stock price (or equity value) provides a key information in measuring the credit risk under the structural model, and we try to build the relationship of stock price and default probability. First,in our one factor model, we use CRR tree to model the stock price’s process and assume that short rate is constant. The Black and Cox(1976) first passage model is used to model the default event. We price convertible bond by the backward induction on the resulting tree model. In our two factor model, we model the stock price and the interest rate by CRR tree and Hull-White tree, and merge these two tree structures and the default process into one tree model for pricing convertible bonds. We also follow Brennan & Schwartz(1980) assumptions to adjust the stock price after convertible bonds converted into stock. At last, sensitivity analyses are given to analyze the effect of the related parameters like the stock price volatility.