标题: 结构式模型下评价可转换公司债
Pricing Convertible Bonds with Default Risk under the Structural Model
作者: 倪健翔
Ni, Chien-Hsiang
戴天时
Dai, Tian-Shyr
财务金融研究所
关键字: 可转换公司债;股票;公司资产;违约机率;结构式模型;违约门槛;首次通过模型;Vasicek;Fortet Method;convertible bonds;shares;corporate assets;default probability;structural models;default threshold for the first time through the model;Vasicek;Fortet Method
公开日期: 2013
摘要: 近年来讨论可转换公司债的论文,都使用树状结构来模拟股价和短利的变化,像是Hung & Wang(2002)和Chamber & Lu(2007),这些在计算信用风险都是利用Jarrow and Tumbull(1995)提出的缩减式模型(Reduced model),利用在外流通债券去计算信用价差来求出公司的违约机率。然而这并没有考虑到股价高低对公司违约机率的影响。本研究以首次通过模型(First passage time model)与结构式信用风险模型(Structural Model)求出公司价值和债务水准,来计算公司违约的机率。最后研究显示是当股价越高,公司资产相对越高破产的机率低,反之亦然。这些结果是上述论文所无法呈现出来的结果。本文的三维度模型是同时计算股价和短期利率(根据Vasicek model),把CRR tree和Hull-White tree结合在一起。在每一个节点上的股东权益都可以视为以公司资产为标的物的向下失效买权,在随机利率下的向下失效买权价的计算,是利用Collin-Dufresne and Goldstein (2001)所提出的.债券价格是透过倒推法(Backward Induction),求出可转债期初价格。
Many recent papers price convertible bonds with a tree that simulate the evolutions of stock prices and interest rates, like Hung & Wang (2002) and Chamber & Lu (2007). These works follow the reduced-form model of Jarrow and Tumbull (1995) that calibrates a corporation’s default probability with the credit spreads of its outstanding bonds. However, the relationship between the corporation’s stock price and the corporation’s default probability is not considered. This thesis addresses this problem by incorporating the first-passage time model, a popular type of structural credit risk model that models the default event with the evolution of firm value and the debt level. The resulting model suggests that a higher stock price implies a relatively higher corporate value as well as a lower default probability, and vice versa— a good property that is not possessed in aforementioned models.My three-dimensional tree models the evolution of the stock price and the short-term interest rates (following the Vasicek model) with the combination of the CRR tree and the Hull-White tree. The equity value at each tree node can be treated as a down-and-out call option on the corporation value and thus the latter value and hence the default probability can be evaluated by the stochastic-interest-rate option pricing method proposed by Collin-Dufresne and Goldstein (2001). The backward induction is then
used to price convertible bonds.
URI: http://140.113.39.130/cdrfb3/record/nctu/#GT070153931
http://hdl.handle.net/11536/75327
显示于类别:Thesis