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

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.