最有效的齐次波动率估计

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摘要翻译：
我们提出了一个充分利用OHLC（开、高、低、闭）价格的任意随机过程的齐次波动率（和方差）估计的综合理论。为此，我们发展了最有效的逐点齐次OHLC波动率估计的理论，对任何价格过程都有效。我们引入了“拟无偏估计”，它可以处理任何类型的期望约束。我们的理论的主要工具是对给定时间间隔的OHLC价格中所包含的所有信息进行简洁的编码，其形式是高负开、低负开和闭负开的联合分布，对于带漂移的Wiener过程，精确地导出了其解析表达式。可以计算这些分布以产生与潜在对数价格随机过程的任何统计性质相关的最有效的估计量。应用于带漂移的对数价格的Wiener过程，基于高负开、低负开和闭负开联合分布的解析表达式，我们给出了最有效的点状波动率和方差估计的显式解析表达式。与Garman-Klass、Roger-Satchell和极大似然估计进行了比较，证明了新估计的有效性。
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英文标题：
《Most Efficient Homogeneous Volatility Estimators》
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作者：
A. Saichev, D. Sornette, V. Filimonov
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最新提交年份：
2009
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
  We present a comprehensive theory of homogeneous volatility (and variance) estimators of arbitrary stochastic processes that fully exploit the OHLC (open, high, low, close) prices. For this, we develop the theory of most efficient point-wise homogeneous OHLC volatility estimators, valid for any price processes. We introduce the "quasi-unbiased estimators", that can address any type of desirable constraints. The main tool of our theory is the parsimonious encoding of all the information contained in the OHLC prices for a given time interval in the form of the joint distributions of the high-minus-open, low-minus-open and close-minus-open values, whose analytical expression is derived exactly for Wiener processes with drift. The distributions can be calculated to yield the most efficient estimators associated with any statistical properties of the underlying log-price stochastic process. Applied to Wiener processes for log-prices with drift, we provide explicit analytical expressions for the most efficient point-wise volatility and variance estimators, based on the analytical expression of the joint distribution of the high-minus-open, low-minus-open and close-minus-open values. The efficiency of the new proposed estimators is favorably compared with that of the Garman-Klass, Roger-Satchell and maximum likelihood estimators.
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PDF链接：
https://arxiv.org/pdf/0908.1677

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关键词：波动率 distribution Applications Quantitative Econophysics prices 进行 分布 low 联合