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使用指数OU模型推断隐藏的金融波动率

文章 arXiv papers · 作者: Zoltan Eisler et al.
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总结

本研究将波动率视为一种无法直接观察、随时间变化并需根据已观察价格推断的量。研究将价格收益和波动率共同建模为二维扩散过程，并为此类过程中的一大类推导出极大似然程序。研究选用指数Ornstein-Uhlenbeck随机波动率模型估计隐藏的波动率状态，并将该方法应用于道琼斯指数。

研究报告称，估计得到的波动率分布为对数正态分布，与所选模型一致。研究还发现波动率与成交量之间存在幂律关系，指数为0.55；并报告未来收益与当前波动率成正比，这表明收益幅度可能具有可预测性。这些是针对一个指数应用得出的实证发现；所提供的说明没有给出样本期、不确定性估计或样本外交易测试。收益关系涉及收益大小，本身并不能证明存在有利可图的方向性信号。

核心观点

  • 由于价格可观察而波动率不可观察，研究将波动率推断为潜在状态。
  • 研究使用联合扩散模型和极大似然估计程序来推断波动率。
  • 在道琼斯指数应用中，指数Ornstein-Uhlenbeck模型得出的估计波动率分布为对数正态分布。
  • 据报告，估计波动率与成交量之间呈幂律关系，指数为0.55。
  • 报告中当前波动率与未来收益幅度之间的联系，并不能证明方向可预测或交易有利可图。

标签

波动率统计学风险管理股票美国市场
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# Volatility: a hidden Markov process in financial time series


# Volatility: a hidden Markov process in financial time series









The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable and only the price is known. Diffusion theory has many common points with the research on volatility, the key of the analogy being that volatility is the time-dependent diffusion coefficient of the random walk for the price return. We present a formal procedure to extract volatility from price data, by assuming that it is described by a hidden Markov process which together with the price form a two-dimensional diffusion process. We derive a maximum likelihood estimate valid for a wide class of two-dimensional diffusion processes. The choice of the exponential Ornstein-Uhlenbeck (expOU) stochastic volatility model performs remarkably well in inferring the hidden state of volatility. The formalism is applied to the Dow Jones index. The main results are: (i) the distribution of estimated volatility is lognormal, which is consistent with the expOU model; (ii) the estimated volatility is related to trading volume by a power law of the form $σ\propto V^{0.55}$; and (iii) future returns are proportional to the current volatility which suggests some degree of predictability for the size of future returns.

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。