论文标题
粗糙波动的统计推断：minimax理论
Statistical inference for rough volatility: Minimax Theory
论文作者
论文摘要
近年来，粗略的波动模型对定量金融社区引起了极大的兴趣。在此范式中，资产价格的波动率是由hurst参数$ h $值的小数布朗尼运动驱动的。在这项工作中，我们对这些模型进行了严格的统计分析。为此，我们建立了最小值下限，以基于实现的小波来进行参数估计和设计程序。我们值得注意的是，基于N采样数据，我们获得了$ n^{ - 1/（4H+2）} $的最佳收敛速度，该$ H $基于N采样数据，从而扩展了仅针对到目前为止的Case Case $ H> 1/2 $而知的结果。因此，我们确定可以在所有制度中以最佳精度来推断粗糙波动率模型的参数。
Rough volatility models have gained considerable interest in the quantitative finance community in recent years. In this paradigm, the volatility of the asset price is driven by a fractional Brownian motion with a small value for the Hurst parameter $H$. In this work, we provide a rigorous statistical analysis of these models. To do so, we establish minimax lower bounds for parameter estimation and design procedures based on wavelets attaining them. We notably obtain an optimal speed of convergence of $n^{-1/(4H+2)}$ for estimating $H$ based on n sampled data, extending results known only for the easier case $H>1/2$ so far. We therefore establish that the parameters of rough volatility models can be inferred with optimal accuracy in all regimes.
