Volatility of volatility is (also) rough. Issue 5 (15th January 2019)

• Record Type: Journal Article
• Authors: Da Fonseca, José; Zhang, Wenjun
• Is Part Of: Journal of futures markets. Volume 39:Issue 5(2019)
• Page Start: 600
• Page End: 611
• Publication Date: 2019-01-15
• Subjects: fractional Brownian motion -- fractional Ornstein–Uhlenbeck -- high‐frequency data -- long memory -- volatility of volatility persistence -- volatility of volatility smoothness; Commodity exchanges -- Periodicals; Foreign exchange futures -- Periodicals; 332.632
• DOI: 10.1002/fut.21995
• Languages: English
• ISSNs: 0270-7314

Abstract

Abstract: Using high‐frequency data for major volatility indexes, we compute the volatility of volatility and show that its logarithm follows a fractional Brownian motion with Hurst parameter smaller than 1/2 thereby extending to the volatility asset class the recent findings obtained for the equity index markets. The results confirm that the volatility of volatility is a rough process and it possesses the long memory property. We also show that the correlation between the volatility and the volatility of volatility is positive, consistent with observations in the volatility option market. Lastly, a robustness check using volatility futures confirms the findings.