English

运筹学学报 ›› 2019, Vol. 23 ›› Issue (4): 124-130.doi: 10.15960/j.cnki.issn.1007-6093.2019.04.011

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随机利率下基于Tsallis熵分布的幂式期权定价

未倩, 王永茂*   

  1. 燕山大学理学院, 河北秦皇岛 066004
  • 收稿日期:2016-12-16 发布日期:2019-12-04
  • 通讯作者: 王永茂 E-mail:mrymw@ysu.edu.cn
  • 基金资助:
    国家自然科学基金（No.11771346）

Pricing of power european options based on Tsallis entropy under stochastic interest rate

WEI Qian, WANG Yongmao*   

  1. School of Science, Yanshan University, Qinhuangdao 066004, Hebei, China
  • Received:2016-12-16 Published:2019-12-04

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摘要： 考虑到无风险利率的随机性以及股票收益率分布的尖峰厚尾和长期相依性，利用具有长程记忆及统计反馈性质的Tsallis熵分布建立股票价格的运动模型，在无风险利率服从Vasicek模型下，运用保险精算定价法得到了幂式期权的定价公式，推广了经典的Black-Scholes定价公式，扩展了已有文献的结论.

关键词: Tsallis熵, Vasicek模型, 幂式期权, 保险精算定价法

Abstract: The randomness of interest and characteristics of fat-tailed, long-term dependence of return distribution of asset prices are considered. Thus, the distribution of Tsallis entropy, which has the characteristics of long-term memory and statistical feedback, is selected to describe the law of the asset prices movement. By using the actuarial approach method under the Vasicek interest rate model, the pricing formulas of power European options are obtained. The formulas not only generalize the classical Black-Scholes conclusion, but also contain the conclusions in the other literature.

Key words: Tsallis entropy, Vasicek interest rate model, power options, actuarial approach method

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