在縮減式信用風險模型評價可轉換公司債之強固樹狀結構

Abstract

本研究之目的為改進Chambers and Lu（2007）之可轉換公司債券評價模型，此模型在切割期數變大時會產生機率為負的問題。本研究將運用Dai（2009）所提出之Stair Tree三元樹接點方法加以修正並提出一個更合理的評價模型。此外，公司違約時之資產回收率（Recovery Rate）在Chambers and Lu（2007）評價模型假設為一常數，本研究以Altman et al.（2005）之違約機率與資產回收率回歸關係式以及Hull , Predescu and White（2005）所提出之真實世界和風險中立世界違約機率關係建構內生資產回收率，觀察此內生資產回收率對可轉換公司債價格造成之影響。

This thesis extends the convertible bond pricing model proposed by Chambers and Lu (2007). They model the evolution of the stock price and the short rate process using the Cox-Ross-Rubinstein tree (1979) and Black-Derman-Toy interest rate tree (1990). The default risk is modelled by the Jarrow and Turnbull (1995) default intensity model. However, there will exist negative branching probabilities when number of steps becomes large. We apply Stair Tree (2009) to fix this anomaly. Beside, the recovery rate is assumed as a constant in their model. We use the regression model introduced by Altman et al. (2005) to find the implied recovery rate. At last, we provide sensitivity analyses to describe the effects of the exogenous parameters on the convertible bond’s price.