Valuing the Callable Convertible Discount Bonds with Credit Risk: An Equivalent Decomposition Method

In the Black-Scholes framework, by employing exotic options instead of plain options, this paper equivalently decomposed the callable convertible discount bonds (CCDB) with credit risk into the portfolio of five kinds of simple securities: two kinds of regular American binary calls with immediately-made fixed payments, one kind of regular up-and-out calls, one kind of regular American binary calls with fixed payment deferred until maturity and one kind of corresponding discount bonds. Then, its analytic valuation formula was worked out. Compared with the existing numerical procedures, this method can not only give new insight of its value composition, but also greatly speed up its valuation.