摘要
复合期权是一类以期权作为标的物的奇异型合约,它已广泛应用于许多金融实践。本文在股价满足一类随机波动率及跳跃均存在于股价和波动率的仿射跳跃扩散模型下(也称随机波动率混合跳跃扩散模型)考察了复合期权的定价。应用二维特征函数和Fourier反变换方法获到了标的为欧式标准看涨期权的欧式复合看涨期权的定价半封闭公式,并将其应用于推导扩展期权的定价。最后,借助于离散快速Fourier变换法(FFT)数值计算定价公式,并用数值实例分析了期权价格对波动率的敏感性。数值结果表明扩散波动和跳跃波动对期权价格都有正的影响,而且跳跃波动的冲击非常显著。
A compound option is a exotic contract whose underlying asset is an option,this option has widely been applied in many financial practice.This paper addresses the pricing of the compound option when the stock＇s price follows an affine jump-diffusion model in which stochastic volatility and jumps in both stock＇s price and volatility are considered,i.e.,stochastic volatility hybrid jump-diffusion model.By using bivariate characteristic functions and the Fourier inversion transform,we obtain an semi-analytical pricing formula for the price of the European compound call option written on an European vanilla call option in this model.We then apply the result to price extendible option.Finally,some numerical examples are provided to analyze the impacts of parameters of volatility on option price by adopting discrete Fast Fourier Transform method to implement the pricing formula.Numerical examples show that volatilities in both diffusion and jumps have positive effects on option prices,and volatility in jumps has very significant impacts.
出处
《数理统计与管理》
CSSCI
北大核心
2015年第5期910-922,共13页
Journal of Applied Statistics and Management
基金
国家自然科学基金(11301099)
教育部人文社会科学研究规划基金项目(13YJA910003)
广西自然科学基金项目(2013GXNSFAA019005)
广西教育厅科学技术研究重点项目(2013ZD010)资助
关键词
复合期权
随机波动率跳扩散模型
FFT
Compound option
Stochastic volatility jump-diffusion model
Fast Fourier Transform method
