Cox-Ingersoll-Ross债券定价模型的推广

An Extention of the Cox-Ingersoll-Ross Bond-pricing Model

债券一直被认为是一种风险较低,收益稳定的投资对象.债券融资是直接融资的一种重要方式.债券定价的高低直接影响到发行人的融资成本和投资人的获利空间.随着我国债券市场的发展,如何对其进行定价是当前金融市场研究的核心内容.Cox-Ingersoll-Ross债券定价模型假定即期利率服从扩散过程,利率长期均值为常数.基于此模型对其进行推广,假设利率的长期均值θ遵循一个离散跳跃过程,跳跃的次数与幅度由中央银行根据物价指数确定,建立一个新的模型,运用引理和资本资产定价模型给出到期日价值为1的零息票债券的定价公式.

Bonds has always been considered as a less risky investment with stable income. Financing by bond is one of the most important direct financing methods. The overpricing or underpricing of Bonds affect the financing cost to issuers and the profit of the investors. In the development of Chinese bonds, it is the kernel that how to price them in the financial market. The bond-pricing model of Cox-Ingersoll-Ross assumes that the short rate following diffusion process and the long-run mean of it is fixed, we assume the long-run mean that follows a discontinous jump process is not fixed in this paper. The central bank determines the number and size of jumps per unit time through the general price level. Under this assumption,we build a new model,then use Ito Lemma and capital asset pricing to give the bond-pricing formula of discounted bond.with a face value of 1 yuan.