约化框架下带有信用风险的永久可转债定价

Pricing of Perpetual Convertible Bonds with Credit Risk Under Framework of Reduce Form

摘要:

将信用风险引入到可转债的定价中,通过修改股票价格的运动过程,得到了一个具有违约风险的股票价格运动过程,然后将其转化为风险中性测度下的运动过程.通过将回收率直接引入到贴现现金流中,得到了可违约永久可转债价格的变分不等方程,并求出了该变分不等方程的显式解.同时对于可回购的可转债,根据息票率的范围,可转债的定价分为3大类,并分别求出每类可转债的价格.最后指出,无论是否具有回购条款,可违约可转债的价格和无违约可转债的价格是相容的.

Abstract:

By modifying the dynamics of stock price,a SDE of stock price with default risk is obtained,and transformed to an adjusted SDE in neutral-risk world.Computing the cash flow by containing the recovery,a variational inequality is derived,and then based on the equation,an explicit solution is obtained.For the convertible bond with call provision,the price of bond is categorized into three classes based on the range of coupon rate,and then three equations can be explicitly solved.Results show that the price of convertible bond with default risk is consistent with that without default risk,regardless of call provision.