Vasicek债券定价模型的推广形式

V asicek债券定价模型假定即期利率r(t)遵循O-U过程,利率的长期均值θ为一个常数.对此进行推广,假设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Ito引理和无套利原理给出到期日价值为1的零息票债券的定价公式.

An Augmentation of the Vasicek Bond-Pricing Model

The bond-pricing model of Vasicek assumes that the short rate of interest of r is mean-reverting Ornstein-Uhlenbeck(O-U)process,and the long-run mean is fixed.In this paper we assume the long-run mean is not fixed,it follows a discontinuous jump process.The central bank determines the number and size of jumps per unit time through the general price level.In this assumption,we build a new model,then use Ito Lemma and Noarbitrage Theory give the bond-pricing fomular of discounted bond with a face value of 1 yuan.