基于违约风险的三叉树模型在可转债定价中的应用研究

Trinomial Tree with Default Risk and Its Application to Pricing Convertible Bonds

本文考虑可转债券的违约风险,研究如何用违约风险下的三叉树模型对可转换债券进行定价。首先本文使用Black-Scholes公式测算企业在单位时间内的违约概率。其次,在计算可转债的债券价值时,将相似经营业绩和同等风险的企业债券收益率作为贴现率,计算现金流的现值,以反映相应的违约风险;在计算可转债看涨期权价值时,本文在三叉树模型中引入违约概率,重新计算调整后股票上涨、下跌的幅度和概率,得到基于违约风险的三叉树定价模型;最后对中国市场中实际的可转债——新钢转债进行了定价的计算,并对结果进行了探讨。

This paper considers default risk of convertible bonds, and studies pricing convertible bonds using trinomial tree with default risk. Firstly, this paper uses Black-Scholes model to calculate default rate of the enterprises. Secondly, when we compute bond value of convertible bonds, future cash flow is discounted using return rate of enterprises with similar operation performance and risk rather than free risk rate to reflect default risk. Finally, when we calculate call option value of convertible bonds, default risk is considered when trinomial tree is used for pricing. Therefore, formulas for rise and fall probability are adjusted. The last part is the case study for convertible bonds of Xinyu Steel in Chinese market, and we get some conclusions after discussion.