Examining Volatility Roughness in the Japanese Stock Market

This study examines the existence of rough volatility, which has recently attracted considerable attention and is characterized by volatility dynamics that cannot be fully captured by conventional volatility models. Specifically, we investigate whether the observed roughness in volatility is merely an artifact induced by microstructure noise inherent in high-frequency price data, or whether such rough behavior persists even after accounting for the effects of noise. The empirical analysis utilizes high-frequency data from the Nikkei 225 index as well as two representatives, actively traded individual stocks. Applying several representative volatility estimation methods, we first construct volatility series and then estimate their Hurst exponents using a nonparametric estimation procedure proposed in the literature. Our results show that, regardless of the presence of microstructure noise, the estimated Hurst exponents consistently take low values, suggesting that the volatility processes under study exhibit rough behavior. These findings provide supporting evidence for the necessity of incorporating roughness into volatility modeling to achieve a more refined understanding of volatility dynamics in financial markets.