# Detecting Rough Volatility: A Filtering Approach

## TL;DR

This paper introduces a filtering approach to estimate unobservable historical volatility of asset prices from high-frequency data, addressing challenges posed by rough volatility models and leveraging fractional Brownian motion representations.

## Contribution

It proposes a novel filtering method using particle techniques to efficiently estimate volatility in rough stochastic models, improving inference in financial econometrics.

## Key findings

- Effective estimation of volatility from high-frequency data.
- Demonstrated applicability to rough volatility models.
- Enhanced inference accuracy over traditional methods.

## Abstract

In this paper, we focus on the estimation of historical volatility of asset prices from high-frequency data. Stochastic volatility models pose a major statistical challenge: since in reality historical volatility is not observable, its current level and, possibly, the parameters governing its dynamics have to be estimated from the observable time series of asset prices. To complicate matters further, recent research has analyzed the rough behavior of volatility time series to challenge the common assumption that the volatility process is a Brownian semimartingale. In order to tackle the arising inferential task efficiently in this setting, we use the fact that a fractional Brownian motion can be represented as a superposition of Markovian semimartingales (Ornstein-Uhlenbeck processes) and we solve the filtering (and parameter estimation) problem by resorting to more standard techniques, such as particle methods.