基于跳扩散过程的数字幂交换期权定价  

Digital Power Exchange Option Pricing under Jump-diffusion Model

作　　者：李文汉 钟盈 吕桂稳 LI Wen-han;ZHONG Ying;LV Gui-wen(College of Mathematics and Physics,Hebei GEO University,Shijiazhuang 050031;Department of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang 050043)

机构地区：[1]河北地质大学数理学院,石家庄050031 [2]石家庄铁道大学数理系,石家庄050043

出　　处：《工程数学学报》2021年第2期257-270,共14页Chinese Journal of Engineering Mathematics

基　　金：河北省社会科学基金(HB19YJ055).

摘　　要：本文提出了一个新型期权称为数字幂交换期权.这种期权是在幂交换期权的基础上,在其损益函数上增加了一个关于两种标的资产幂函数比值范围的示性函数.该期权可以规避由于两个标的资产价格偏差过大所带来的损失.然后,通过选择不同的计价单位,构造具有跳扩散过程的标的资产的价格过程,推导出了数字幂交换期权的价格公式.最后,借助两支股票的调整后收盘价的历史数据,讨论了数字幂交换期权的价格过程.In this paper,we propose a new option named as digital power exchange option by adding an indicator function of the ratio of the two underlying assets prices(denoted power forms)to the payoff of the power exchange option.This proposed model can be used to avoid the risk caused by the excessive price deviation of two underlying assets.Based on the above work,we obtain the explicit pricing formulas of the digital power exchange option under the jump-diffusion model by choosing the different numeraire.Finally,we take some historical data of the adjusted closing prices of two real stocks to discuss the prices of the digital power exchange option.

关 键 词：数字幂交换期权 规避风险 跳扩散过程 ESSCHER变换 数值分析 

分 类 号：O211.6[理学—概率论与数理统计]