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可违约债券在随机波动率假定下近似定价公式的求解
引用本文:陈侃,李时银.可违约债券在随机波动率假定下近似定价公式的求解[J].数学研究,2005,38(3):321-332.
作者姓名:陈侃  李时银
作者单位:厦门大学数学学院,福建,厦门,361005
摘    要:在假设标的资产价格的波动率是一个快速均值回复OU过程的函数的条件下,导出相应的可违约债券价格公式所应满足的偏微分方程,并利用Taylor级数展开得到一组Poisson方程.求解这些方程,得到非完全市场下固定补偿率的债券价格的近似表达式,然后在不同的补偿率规定上作了一些修正和推广.

关 键 词:随机波动率  快速均值回复  非完全市场  可违约债券
修稿时间:2004年12月30

An Approximate Price Formula of Defaultable Bond with Stochastic Volatility
Chen Kan,Li Shiyin.An Approximate Price Formula of Defaultable Bond with Stochastic Volatility[J].Journal of Mathematical Study,2005,38(3):321-332.
Authors:Chen Kan  Li Shiyin
Abstract:In this paper, we will establish a Credit-Risky model assuming that the volatility of the underlying risky asset price is a function of the fast mean-reverting OU process. Then, we can derive a partial differential equation to price a defaultable zero-coupon bond according to it. Furthermore we will derive an approximate solution of this equation as the price formula of defaultable bond under the incomplete market by using Taylor series expansion and the methods of solving Poisson equation. At last, we will generalize the result to a different payment function.
Keywords:stochastic volatility  fast mean-reverting  incomplete market  defaultable zero-coupon bond  
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