具有价格随机波动率的新型期权定价  

The Pricing of Exotic Options under Stochastic Volatility

作　　者：吴恒煜[1] 吴唤群[2] 

机构地区：[1]江西财经大学金融学院 [2]广州大学经济与管理学院,广东广州510006

出　　处：《系统工程》2008年第2期20-24,共5页Systems Engineering

基　　金：教育部人文社会科学一般项目(06JA790025);江西省教育厅科技计划项目(赣教技字[2007]261);广东省自然科学基金资助项目(0530055705003980);江西财经大学“金融深化过程中信用风险的测度与控制”创新团队基金(江财科研[2005]4)

摘　　要：为了研究具有随机波动率的新型期权的定价,应用近似方法分析随机波动率期权的价格。模型允许基础资产价格具有均值回复特征与波动率具有平方根过程,得出关于平均波动率新型期权泰勒展开式。平均波动率交叉矩通过常微分方程的F roben ius展开得到,并给出一些新型期权的定价公式,结果表明该近似方法在给具有价格随机波动率的新型期权的定价时非常准确与有效。In order to analyze the pricing of exotic options under Stochastic Volatility, this paper uses an approximation to price exotic options within a stochastic volatility framework. Assuming a general mean reverting process for the underlying asset and a square-root process for the volatility, the paper points out an approximation for option prices using a Taylor expansion around two average defined volatilities. The cross-moments of the average volatilities are computed analytically at any order using a Frobenius series solution to some ordinary differential equation. Furthermore, the paper Prices soroe exotics such as barrier and digital barrier options. The conclusion shows that the approximation has been found to be very efficient and convergent at the pricing of exotic options under stochastic volatility.

关 键 词：期权定价 新型期权 数值障碍期权 随机波动率 

分 类 号：F830[经济管理—金融学]