基于带跳随机波动率模型的双币种重置期权定价研究  

Pricing Quanto Rest Options in a Stochastic Volatility Model with Jump Risks

作　　者：韦铸娥 何家文[2] WEI Zhu-e;He Jia-wen(College of Information Engineering,Nanning University,Nanning 530200,China;School of Foundational Education,Nanning University,Nanning 530200,China)

机构地区：[1]南宁学院信息工程学院,广西南宁530200 [2]南宁学院公共教学部,广西南宁530200

出　　处：《数学的实践与认识》2020年第3期48-59,共12页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11461008);广西高校中青年教师科研基础能力提升项目(2019KY0940);南宁学院校级科研项目(2018XJ44);南宁学院教授培育工程项目(2019JSGC11).

摘　　要：研究了外国标的资产价格,汇率及其波动率过程满足仿射跳扩散模型的双币种重置期权定价问题,其中波动率过程与标的资产,汇率相关,且具有共同跳跃风险成分.利用多维Feynman-Kac定理,Fourier逆变换等方法,获得了双币种重置期权价格的表达式.应用数值计算分析了波动率过程主要参数对期权价格的影响.数值结果表明,波动率因素以及跳跃风险参数对期权价格的影响是显著的.The pricing of the Quanto Rest options is considered under an affine jump diffusion model by introducing jump risks in stochastic volatility,the foreign underlying asset pricing and the exchange rate process.The underlying asset and exchange rate are assumed to be correlated and have simultaneous correlated jumps with the volatility.Using the multidimentional Feynman-Kac theorem and the Fourier inversion transform,the formulas for price of the Quanto Rest call options are obtained.Finally,some numerical experiments are provided to analyze the impacts of the key parameters in this stochastic volatility model on the option prices.Numerical results show that the volatility factors and the simultaneous correlated jumps in this proposed model have significant impacts on options values.

关 键 词：跳扩散模型 随机波动率 双币种重置期权 Fourier逆变换 

分 类 号：F830.9[经济管理—金融学]