相关实验视频
Updated: Jun 28, 2025

04:58
A Rapid Method for Modeling a Variable Cycle Engine
Published on: August 13, 2019
7.6K
一个由霍克斯过程驱动的玛奥恩斯坦-乌伦贝克模型
Guillaume Bernis1, Riccardo Brignone2, Simone Scotti3
1Natixis Assurances, Paris, France.
概括
我们引入了一种新的金融模型,将OU Barndorff-Nielsen和Shephard模型扩展到包括使用霍克斯过程的跳跃集群. 这种增强的模型更好地捕捉了市场动态,特别是VIX期权,显示了上升的隐性波动倾斜.
科学领域:
- 量化金融 量化金融
- 随机过程 随机过程
- 金融建模金融建模
背景情况:
- -OU Barndorff-Nielsen和Shephard模型是金融计量经济学的基石,但缺乏捕捉跳跃集群的能力.
- 跳跃集群现象显著影响资产价格动态和期权定价,需要更复杂的模型.
研究的目的:
- 通过使用霍克斯过程将跳跃集群纳入OU Barndorff-Nielsen和Shephard模型的扩展.
- 分析这个新的-OU-霍克斯模型的数学特性和财务影响.
- 为了证明模型的改进灵活性和校准能力.
主要方法:
- 扩展-OU模型与跳跃集群的霍克斯过程.
- 应用连续状态分支过程与SDE解决方案的移民.
- 开发一种自我激发的Esscher类型测量变化,用于风险中立的动态.
- 为了分析解决方案,利用亲属性 (拉普拉斯变换,二次变化).
- 校准使用市场价格和特有的函数反转.
主要成果:
- 对于资产价格SDE的强有力的解决方案的存在和独特性.
- 关键金融量 (如日志回报拉普拉斯变换和方差分布) 的明确形式.
- 与具有相当参数数量的标准OU模型相比,显示了更大的灵活性.
- 成功对市场数据进行校准,并开发精确的模拟方案.
- 观察到VIX期权的上升式暗示波动,与OU模型的下降倾斜形成鲜明对比.
结论:
- 拟议的-OU-Hawkes模型有效地捕捉了跳跃集群,在金融建模中提供了更大的灵活性.
- 该模型提供了更现实的市场行为表现,特别明显在VIX期权的隐含波动性.
- 这一框架为复杂的金融市场的定价和风险管理提供了重大进展.
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