论文标题
粗暴的波动：事实还是人工制品？
Rough volatility: fact or artefact?
论文作者
论文摘要
我们研究了使用无模型方法使用“粗糙”分数流程$ h <0.5 $的统计证据。我们介绍了一种非参数方法，用于使用沿划分序列的归一化$ p $ th变化的概念来估计基于离散样本的函数的粗糙度。我们使用详细的数值实验基于分数布朗运动和其他分数过程的详细数值实验，研究了估计量的有限样本性能，以测量随机过程的样本路径的粗糙度。然后，我们将此方法用于估计基于高频观察的实现波动率信号的粗糙度。基于随机波动率模型的详细数值实验表明，即使瞬时波动性具有与布朗运动相同的粗糙度的扩散动力学，实现的波动率也表现出与hurst指数相对应的粗糙行为，明显小于$ 0.5 $。比较具有不同值的分数波动率模型中实现和瞬时波动率的粗糙度估计值表明，无论斑点波动过程的粗糙度如何，实现的波动率总是表现出具有明显的Hurst Index $ \ hat {H} <0.5 $的“粗糙”行为。这些结果表明，在实现的波动时间序列中观察到的粗糙度的起源在于微观结构噪声，而不是波动性过程本身。
We investigate the statistical evidence for the use of `rough' fractional processes with Hurst exponent $H< 0.5$ for the modeling of volatility of financial assets, using a model-free approach. We introduce a non-parametric method for estimating the roughness of a function based on discrete sample, using the concept of normalized $p$-th variation along a sequence of partitions. We investigate the finite sample performance of our estimator for measuring the roughness of sample paths of stochastic processes using detailed numerical experiments based on sample paths of fractional Brownian motion and other fractional processes. We then apply this method to estimate the roughness of realized volatility signals based on high-frequency observations. Detailed numerical experiments based on stochastic volatility models show that, even when the instantaneous volatility has diffusive dynamics with the same roughness as Brownian motion, the realized volatility exhibits rough behaviour corresponding to a Hurst exponent significantly smaller than $0.5$. Comparison of roughness estimates for realized and instantaneous volatility in fractional volatility models with different values of Hurst exponent shows that, irrespective of the roughness of the spot volatility process, realized volatility always exhibits `rough' behaviour with an apparent Hurst index $\hat{H}<0.5$. These results suggest that the origin of the roughness observed in realized volatility time-series lies in the microstructure noise rather than the volatility process itself.
