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

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.