推广的Vasicek利率模型在衍生证券定价分析中的应用

The Extended Vasicek Interest Model in Derivative Security Pricing with Its Applications

在分析Vasicek利率模型的基础上,将利率的长期均值,瞬时波动率和均值回复率为常数的情形推广为随时间t而变化的确定性函数,得到一种新的Vasicek利率模型.利用Ito引理和构建债券组合策略求得推广的Vasicek利率模型下债券价格满足的偏微分方程,进而得出了该模型下到期日为T,到期时支付1元的折价债券定价模型及债券选择权.

Based on analyzing the Vasicek stochastic interest model, we transform the long-run mean,the fluctuation rate and the mean restoration which are constant into fixed functions about t. In this assumption, we build a new model by solving a partial differential equation based on the Extended Vasicek interest model. Furthermore, we give the bond-pricing formula of discounted bond-choose with a face time T and pay one Yuan by using Ito Lemma and build the constitute of the bond.