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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 ›› 2024, Vol. 41 ›› Issue (1): 17-38.doi: 10.3969/j.issn.1005-3085.2024.01.002

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基于跳聚集现象随机波动率短期利率模型的影响研究

张新军1,  江  良2,  林  琦2,  宋丽平3   

  1. 1. 莆田学院 金融数学福建省高校重点实验室，莆田 351100;
    2. 莆田学院 福建省金融信息处理重点实验室，莆田 351100;
    3. 莆田学院 应用数学福建省高校重点实验室，莆田 351100
  • 收稿日期:2021-03-24 接受日期:2021-07-30 出版日期:2024-02-15 发布日期:2024-04-15
  • 通讯作者: 江良 E-mail: ptjliang@163.com
  • 基金资助:
    福建省自然科学基金 (2020J01907; 2021J011102)；福建省社会科学基金 (FJ2018B065).

The Impact of Self-exciting Jump Process for the Short Term Model with Stochastic Volatility

ZHANG Xinjun1,  JIANG Liang2,  LIN Qi2,  SONG Liping3   

  1. 1. Key Laboratory of Financial Mathematics of Fujian Province University, Putian University, Putian 351100;
    2. Fujian Key Laboratory of Financial Information Processing, Putian University, Putian 351100;
    3. Key Laboratory of Applied Mathematics of Fujian Province University, Putian University, Putian 351100
  • Received:2021-03-24 Accepted:2021-07-30 Online:2024-02-15 Published:2024-04-15
  • Contact: L. Jiang. E-mail address: ptjliang@163.com
  • Supported by:
    The Natural Science Foundation of Fujian Province (2020J01907; 2021J011102); the Social Science Foundation of Fujian Province (FJ2018B065).

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摘要：

构建了具有自我激励机制跳的随机波动率短期利率模型，应用Hawkes过程描述自我激励机制的跳，从而刻画了跳的聚集现象。基于微分算子展开给出精确的矩函数，进一步应用广义矩方法给出模型的参数估计值和统计推断。实证结果揭示了在随机波动模型条件下，引入自我激励机制跳的模型将不会明显地改变了拟合效果，但是在统计意义上接受强度满足Hawkes过程，而且所构建的模型也能很好地刻画跳的聚集现象。最后，使用过滤方法给出随机波动率、跳的幅度、跳的概率和随机跳强度的估计，特别是跳的概率估计值可作为市场压力测试的一个重要指标。

关键词: 短期利率模型, 随机波动率, 跳的聚集, Hawkes过程

Abstract:

The stochastic volatility and self--exciting jump process are incorporated into a short-rate model. In the model, the self-exciting jump process will modeled by a Hawkes process, which captures the jump cluster. The expansion of the differential operator is applied to compute the closed-form moment function, and further develop the general moment method to estimate the parameters in the model and make statistical inference. The empirical results provide that there is no enough evidence to support the goodness of fit test. But the model with Hawkes process is significance in statistics, and  could strongly capture the jump clustering. Finally, the filtered values are estimated for the stochastic volatility, jump size, jump probability and intensity of jump by using filtering method. It is worth mention that the filtered jump probability is a plausible indicator to measure financial market stress.

Key words: short term model, stochastic volatility, jump clustering, Hawkes process

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