华东师范大学学报(自然科学版) ›› 2017, Vol. ›› Issue (3): 29-38.doi: 10.3969/j.issn.1000-5641.2017.03.003

• 数学 • 上一篇    下一篇

混合分数跳-扩散模型下的亚式期权定价

耿延静, 周圣武   

  1. 中国矿业大学 数学系, 江苏 徐州 221008
  • 收稿日期:2016-06-23 出版日期:2017-05-25 发布日期:2017-05-18
  • 通讯作者: 周圣武,男,教授,研究方向为金融数学.E-mail:zswcumt@163.com E-mail:zswcumt@163.com
  • 作者简介:耿延静,女,硕士研究生,研究方向为金融数学.E-mail:gengyanjing_ah@qq.com
  • 基金资助:
    中央高校基本科研业务费专项资金(2013XK03)

Pricing Asian option under mixed jump-fraction process

GENG Yan-jing, ZHOU Sheng-wu   

  1. Department of Mathematics, China University of Mining and Technology, Xuzhou Jiangsu 221008, China
  • Received:2016-06-23 Online:2017-05-25 Published:2017-05-18

摘要: 给出了标的资产服从混合分数跳-扩散过程的几何平均亚式期权定价的解析解.运用广义Itô引理和自融资交易策略得到混合分数布朗运动下带跳的几何平均亚式期权定价的偏微分方程模型.结合边值条件,通过求解该偏微分方程得到亚式期权定价的解析解.通过数值试验,讨论各定价参数对期权价值的影响.本文推广了一些已有的结论,所得结果更贴近实际金融市场.

关键词: 混合分数跳-扩散过程, 几何平均亚式期权, 偏微分方程

Abstract: This paper mainly studied the geometric average Asian option pricing on the condition that the underlying asset followed mixed jump-fraction process. The general Itô's lemma and the self-financing dynamic strategy were obtained by using the partial differential equation of such option pricing in the mixed fractional environment with jump. With the combination of boundary condition, an analytic formula for the geometric average Asian option was derived by solving the partial differential equation. The numerical experiments were showed to discuss the influence of different parameters on the option value. The results were the generalization of some existing results which was closer to the real financial market.

Key words: mixed jump-fraction process, geometric average Asian option, partial differential equation

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