跳至正文
返回文库全部文档

波动率分布如何塑造金融收益尾部

文章 arXiv papers · 作者: Hernán Larralde et al.
阅读原文

总结

本文研究收益分布，并假设在给定时变方差后，收益相互独立。由于波动率本身会随机变化，总收益分布会反映这些波动率水平的分布。作者推导出一种尺度形式，直接将收益分布形态与波动率分布形态联系起来。

该框架将收益的幂律尾部解释为波动率的幂律尾部所致，并将比特币的拉伸指数型收益分布与形态类似的波动率分布联系起来。文中所述检验使用S&P 500指数数据、苹果和派拉蒙的股票数据以及比特币数据。该方法为观察到的分布形态提供了统计解释，但依赖条件独立假设和对波动率行为的假定；摘要没有证明这些假设涵盖了市场中的所有依赖关系或尾部风险来源。

核心观点

  • 模型假设在给定时变方差后，收益相互独立。
  • 波动率分布决定收益的尺度形式和形态。
  • 波动率的幂律尾部可能导致收益出现幂律尾部。
  • 该框架将比特币的拉伸指数型收益与拉伸指数型波动率联系起来。
  • 研究在指数、个股和比特币数据上检验这些预测，但结论受模型假设限制。

标签

统计学波动率加密资产股票
全文
# Scaling and shape of financial returns distributions modeled as conditionally independent random variables


# Scaling and shape of financial returns distributions modeled as conditionally independent random variables









We show that assuming that the returns are independent when conditioned on the value of their variance (volatility), which itself varies in time randomly, then the distribution of returns is well described by the statistics of the sum of conditionally independent random variables. In particular, we show that the distribution of returns can be cast in a simple scaling form, and that its functional form is directly related to the distribution of the volatilities. This approach explains the presence of power-law tails in the returns as a direct consequence of the presence of a power law tail in the distribution of volatilities. It also provides the form of the distribution of Bitcoin returns, which behaves as a stretched exponential, as a consequence of the fact that the Bitcoin volatilities distribution is also closely described by a stretched exponential. We test our predictions with data from the S\&P 500 index, Apple and Paramount stocks; and Bitcoin.

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。