跳扩散模型下交换期权定价的Mellin变换方法  

Pricing Exchange Options Under Jump-diffusion Models Using Mellin Transform

作　　者：刘朝晖 李翠香[1] LIU Zhao-hui;LI Cui-xiang(School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,河北石家庄050024

出　　处：《数学的实践与认识》2021年第12期82-88,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11571089);河北省教育厅重点基金(ZD2018065,ZD2019053);河北师范大学在读研究生创新能力培养资助项目(CXZZSS2021048)。

摘　　要：在资产价格服从跳扩散模型的条件下,利用Mellin变换的方法对交换期权定价.首先利用Feynman-K ac定理得到了交换期权的价格过程满足的偏积-微分方程.其次利用Mellin变换得到不依赖于跳跃大小分布的交换期权的定价公式.最后通过数值分析检验了此定价公式的准确性,并分析了期权价格与资产价格的关系.In this paper,we use Mellin transform to price the exchange options under the assumption that underlying asset prices follow jump-diffusion processes.First,we derive a partial integro-differential equation satisfied by the price process of the exchange options by the Feynman-Kac theorem.Secondly,we obtain the pricing formula of exchange options using Mellin transform,which does not dependent on the distribution of the jump size.Finally,the accuracy of our pricing formula is verified by numerical example,and we also discuss the relationship between the price of exchange options and asset prices.

关 键 词：跳扩散模型 交换期权 Mellin变换 

分 类 号：F830.9[经济管理—金融学]