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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2021, Vol. 38 ›› Issue (2): 257-270.doi: 10.3969/j.issn.1005-3085.2021.02.009

• • 上一篇    下一篇

基于跳扩散过程的数字幂交换期权定价（英）

李文汉1,   钟   盈1,   吕桂稳2   

  1. 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
  • 收稿日期:2020-06-16 接受日期:2020-09-09 出版日期:2021-04-15 发布日期:2022-11-08
  • 通讯作者: 吕桂稳 E-mail: lvguiwenyy@126.com
  • 基金资助:
    The Social Science Foundation Project of Hebei Province (HB19YJ055).

Digital Power Exchange Option Pricing under Jump-diffusion Model

LI Wen-han1,   ZHONG Ying1,   LV Gui-wen2   

  1. 1- College of Mathematics and Physics, Hebei GEO University, Shijiazhuang 050031
    2- Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043
  • Received:2020-06-16 Accepted:2020-09-09 Online:2021-04-15 Published:2022-11-08
  • Contact: G. Lv. E-mail address: lvguiwenyy@126.com
  • Supported by:
    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．

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

Abstract: 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.

Key words: digital power exchange option, avoid risk, jump-diffusion process, Esscher transform, numerical analysis

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