含权债券定价的统一框架及其数值分析

The Unified Framework and Numerical Analysis of the Bond with Option

本文从理论上推导了一般债券定价的偏微分方程,详细分析了包含欧式和美式看涨和看跌期权的4类债券,并给出了4类含权债券定价的边界条件。利用隐性差分法数值求解了偏微分方程,针对4类期权对不同利率参数的敏感性进行了分析。

In this paper, we first derive the pricing partial differential equation for the generic bond theoretically; analyze four kinds of bonds with embedded option, i.e. the European call and put option, the American call and put option, the pricing boundaries of these four kinds of option are also introduced. Then we solve the equation with implicit difference methods and analyze the sensitivities of these four options with the changes of the parameters of the interest rate models.