A New Proxy for Estimating the Roughness of Volatility

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.