# Volatility is rough

**Authors:** Jim Gatheral, Thibault Jaisson, Mathieu Rosenbaum  
**arXiv:** [1410.3394](https://arxiv.org/abs/1410.3394)  
**Date:** 2014-10-13  
**Summary page:** https://www.summarizepaper.com/en/paper/1410.3394v1/

## Key points

- Authors Gatheral, Jaisson, and Rosenbaum explore volatility estimation using high-frequency data
- Log-volatility behaves like a fractional Brownian motion with Hurst exponent H around 0.1 across various time scales
- Introduction of Rough FSV (RFSV) model with H less than 1/2 for enhanced volatility forecasting
- RFSV model consistently improves forecasts of realized volatility compared to traditional methods
- Long memory in volatility acknowledged as a stylized fact in financial markets but not present in RFSV model
- Importance of considering market microstructure when studying volatility dynamics
- Research contributes significantly to understanding market behavior and forecasting techniques in volatile trading environments

## Summary

In their paper titled "Volatility is rough," authors Jim Gatheral, Thibault Jaisson, and Mathieu Rosenbaum delve into the estimation of volatility using recent high-frequency data. They reexamine the smoothness of the volatility process and make a significant discovery that log-volatility behaves akin to a fractional Brownian motion with a Hurst exponent H around 0.1 across various time scales. This observation prompts them to adopt the fractional stochastic volatility (FSV) model proposed by Comte and Renault. However, they introduce their own model called Rough FSV (RFSV), emphasizing that unlike FSV, in RFSV, H is less than 1/2. The authors demonstrate the remarkable consistency of their RFSV model with financial time series data, showcasing its ability to enhance forecasts of realized volatility. Their research offers valuable insights into understanding and modeling volatility dynamics in financial markets . By examining recent high-frequency data , Gatheral et al. show that log-volatility follows a fractional Brownian motion with a Hurst exponent H around 0.1 . This leads them to propose their own model called Rough FSV (RFSV) , which has been shown to consistently improve forecasts of realized volatility. The authors also shed light on why long memory in volatility has been widely acknowledged as a stylized fact in financial markets . Despite not exhibiting long memory in the RFSV model, traditional statistical methods designed to detect volatility persistence often erroneously infer it from data generated by this model. This discrepancy highlights the importance of considering market microstructure , such as high-frequency trading and order splitting, when studying volatility dynamics. Overall, Gatheral, Jaisson, and Rosenbaum's research contributes significantly to advancing our comprehension of market behavior and forecasting techniques in volatile trading environments. Their nuanced analysis and empirical evidence provide a quantitative foundation for understanding the roughness of volatility and its implications for financial markets.