随机波动率跳扩散模型的价差幂期权定价研究  

Research on the Pricing of Spread Power Options in the Stochastic Volatility Jump-Diffusion Model

作　　者：韦铸娥 何家文[2] WEI Zhue;HE Jiawen(College of Information Engineering,Nanning University;College of Artificial Intelligence and Software,Nanning University,Nanning,Guangxi Zhuang Autonomous Region,530200 China)

机构地区：[1]南宁学院信息工程学院 [2]南宁学院人工智能与软件学院,广西南宁530200

出　　处：《科技资讯》2024年第21期228-232,共5页Science & Technology Information

基　　金：广西自然科学基金项目(项目编号:2023GXNSFAA026333);广西高校中青年教师科研基础能力提升项目(项目编号:2022KY1782)。

摘　　要：以价差幂期权定价为研究对象,运用随机波动率模型和跳扩散模型描述市场结构。首先,基于风险中性概率测度,构建了一个模型,该模型假设资产收益率的方差均服从相同的仿射波动结构,同时资产价格遵循跳扩散过程。其次,运用鞅方法和傅里叶变换技术,导出了价差期权的拟闭型定价公式。这一方法为期权定价提供了一种更加精确且有效的工具,不仅丰富了期权定价理论,还对实际金融市场中复杂衍生品的定价具有重要的理论支持和应用价值。Taking the pricing of spread power options as the research object,the article employs stochastic volatility models and jump-diffusion models to describe market structures.Firstly,a model is constructed based on the risk-neutral probability measure,assuming that the variances of asset returns follow the same affine volatility structure,while the asset prices follow a jump-diffusion process.Then,by employing martingale approach and Fourier trans-form technology,a quasi-closed form pricing formula for the spread power option is derived.This method pro-vides a more precise and effective tool for option pricing.It not only enriches the theory of option pricing but also offers substantial theoretical support and practical applications for the pricing of complex derivatives in the actual fi-nancial markets.

关 键 词：价差幂期权 跳扩散模型 随机波动率 随机微分方程 

分 类 号：F224[经济管理—国民经济] F830.9