付息可赎回可转换债券定价解析式:完全拆解法

The Analytic Valuation of Coupon-bearing Callable Convertible Bonds: An Equivalent Decomposition Method

本文利用美式二值买权和上敲出买权等奇异期权,在Black-Scholes期权模型假设框架下,依据风险中性定价原理,将付息可赎回可转换债券“完全拆解”为七种相对简单证券的组合,并且通过这些简单证券的定价解析式推导出其定价解析式。同时,还推导出转息有效价值的解析式。这不仅仅为认知其价值组成提供了一个全新视角,而且相对现有的各种数值定价法,该解析式大大提高了定价效率。

With the help of American binary calls and up-and-out calls, in the Black-Scholes framework, according to the risk-neutral valuation principal, this paper completely decomposes Coupon-bearing Callable Convertible Bonds （CCCB） into the portfolio of seven kinds of simple securities. At the same time, based on the existing valuation formulae for these simple securities, the valuation formula for CCCB is derived. Furthermore, the valuation formula for the effective value of coupons of CCCB is also worked out. Compared with the existing numerical procedures, this method can not only give a lot new insight of the value composition of CCCB, but also greatly speed up the valuation of CCCB.