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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

• • 上一篇    

多维随机波动率模型下欧式离散障碍期权定价

陈有杰1,  温小梅2,  黄  晴3,  邓国和4   

  1. 1. 广东工业大学管理学院，广州 510006
    2. 桂林信息科技学院数学教研部，桂林 541004
    3. 北部湾大学理学院，钦州 535011
    4. 广西师范大学数学与统计学院，桂林 541004
  • 收稿日期:2022-07-27 接受日期:2023-02-26 发布日期:2025-06-15
  • 通讯作者: 邓国和 E-mail: dengguohe@gxnu.edu.cn
  • 基金资助:
    国家自然科学基金(11461008)；广西高校中青年教师科研基础能力提升项目(2022KY1633).

Pricing European Discretely Monitored Barrier Options in Multidimensional Stochastic Volatility Model

CHEN Youjie1,  WEN Xiaomei2,  HUANG Qing3,  DENG Guohe4   

  1. 1. School of Management, Guangdong University of Technology, Guangzhou 510006
    2. Department of Mathematics, Guilin Institute of Information Technology, Guilin 541004
    3. College of Science, Beibu Gulf University, Qinzhou 535011
    4. School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004
  • Received:2022-07-27 Accepted:2023-02-26 Published:2025-06-15
  • Contact: G. Deng. E-mail address: dengguohe@gxnu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (11461008)；the Project for Enhancing the Basic Scientific Research Capacity of Young and Middle-aged Teachers in Guangxi Colleges and Universities (2022KY1633).

摘要：

随着经济全球化的不断发展，我国的金融市场逐渐国际化，金融衍生品市场在我国的金融领域变得越来越重要。期权作为最常见、最重要的金融衍生品之一，是风险管理的核心工具，如何给期权定价，自然是一个非常重要的问题。考虑了实际金融市场的复杂性和资产价格波动的多变性，在标的资产价格满足Wishart多维随机波动率模型下讨论离散时间情形的欧式障碍期权定价。应用半鞅It\^o公式、多维联合特征函数、Girsanov测度变换和Fourier反变换等随机分析技术和数学归纳法，推导出了离散时间情形的欧式障碍期权的定价公式，并给出了该期权的离散快速Fourier(Fast Fourier Transform, FFT)变换法数值计算定价公式。最后给出了数值计算实例，并分析了不同波动率参数下期权隐含波动率曲线的变化规律，结果显示扩散波动因素对期权的价格有显著影响。

关键词: Wishart模型, 障碍期权, Fourier反变换, FFT

Abstract:

As one of the most common and important financial derivatives, options are the core tools of risk management, and how to price options is naturally an important issue. In this paper, the pricing of European barrier options for discrete time scenarios under the model of Wishart multidimensional stochastic volatility is discussed. Using some stochastic analysis techniques and mathematical induction, such as the semi-martingale It\^o formula, multidimensional federated characteristic functions, Girsanov theorem and Fourier inverse transform technique are to derive the pricing formula for the European discrete barrier call option. And derive the discrete fast Fourier transform (FFT) method to implement the pricing formula for the option. Finally, numerical examples are given, and the variation of the implicit volatility curve of options under different volatility parameters is also analyzed by this numerical examples, the results show that the diffusion factor has a significant impact on the price of options.

Key words: Wishart model, barrier option, Fourier inverse transform, FFT

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