跳至正文
返回文库全部文档

均值回归金融模型中的加性噪声与乘性噪声

文章 arXiv papers · 作者: C. Anteneodo et al.
阅读原文

总结

本文提出一种广义随机模型，用于描述倾向于回归历史参考水平的金融变量。模型结合两类维纳过程噪声：一类是受系统内部行为调节的乘性成分，另一类是视为外生的加性成分。作者聚焦于波动率动态，并指出该框架也可能适用于其他均值回归金融变量。他们认为，许多既有方法都是这一广义模型的特例。

分析利用Itô–Langevin方程推导模型的长期概率密度，并考察其形态如何随参数选择而变化。作者报告称，由此得到的一系列分布能够描述整个数据范围内的实证数据。文中未提供具体数据集、参数估计、拟合优度比较统计量或预测与交易检验。因此，所述实证相关性属于建模主张；模型是否适用于特定资产或用途仍需另行评估。

核心观点

  • 模型描述倾向于回归历史参考水平的金融变量。
  • 模型结合与系统行为相关的乘性噪声和外生加性噪声。
  • 该框架聚焦于波动率，也可能适用于其他均值回归金融变量。
  • 研究使用Itô–Langevin形式分析长期概率密度。
  • 不同模型参数会产生多种分布形态，作者称这些形态能够描述实证数据。

标签

波动率均值回归统计学
全文
# Additive-multiplicative stochastic models of financial mean-reverting processes


# Additive-multiplicative stochastic models of financial mean-reverting processes









We investigate a generalized stochastic model with the property known as mean reversion, that is, the tendency to relax towards a historical reference level. Besides this property, the dynamics is driven by multiplicative and additive Wiener processes. While the former is modulated by the internal behavior of the system, the latter is purely exogenous. We focus on the stochastic dynamics of volatilities, but our model may also be suitable for other financial random variables exhibiting the mean reversion property. The generalized model contains, as particular cases, many early approaches in the literature of volatilities or, more generally, of mean-reverting financial processes. We analyze the long-time probability density function associated to the model defined through a Itô-Langevin equation. We obtain a rich spectrum of shapes for the probability function according to the model parameters. We show that additive-multiplicative processes provide realistic models to describe empirical distributions, for the whole range of data.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。