In this paper, we propose a new proxy for the unobserved volatility process that will allow us to better understand and hence model a rough or persistent volatility. Starting with a stochastic volatility model with minimal assumptions on the volatility process, we calibrate the model to options’ data and their sensitivities to obtain an implied volatility process. Starting with this new proxy, we then study the roughness/persistence of the volatility using S&P 500 European put option daily data. We then estimate the Hurst index, i.e., roughness/smoothness parameter, of the volatility with various techniques to find that the volatility does exhibit a rough behavior, even in a low-frequency framework.

中文翻译：

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估计波动率粗糙度的新代理

在本文中，我们提出了一种新的未观察到的波动过程代理，这将使我们能够更好地理解并因此对粗略或持续的波动进行建模。从对波动率过程进行最小假设的随机波动率模型开始，我们根据期权数据及其敏感性来校准模型，以获得隐含波动率过程。从这个新的代理开始，我们使用标准普尔 500 欧洲看跌期权每日数据研究波动性的粗糙度/持续性。然后，我们使用各种技术估计波动率的赫斯特指数，即粗糙度/平滑度参数，发现波动率确实表现出粗糙的行为，即使在低频框架中也是如此。