The Analytic Valuation of the Basic Coupon-bearing Callable Convertible Bonds with Credit Risk: A Probabilistic Method

It´s very difficult for investors to valuate the coupon-bearing Callable Convertible Bond (CCB) with credit risk because of its complex hybrid features. Currently, its analytic valuation formula has not been seen in the existing literatures and it has usually been valuated with numerical procedures whose computing efficiency is not good enough. In this paper, according to the three cases of the future ending of the coupon-bearing CCB with credit risk, for the first time, we perfectly decompose it into three simpler parts corresponding respectively to three cases of the future ending. Then, in the Black-Scholes framework, according as the risk-neutral valuation principle, we derive the closed form solution for the coupon-bearing CCB with credit risk by obtaining the closed solutions for these three parts respectively at first. Compared with the existing numerical procedures, this solution can greatly speed up the valuation