Variance-Gamma and Normal-Inverse Gaussian models: Goodness-of-fit to Chinese high-frequency index returns

• VG and NIG distributions are compared with the benchmark of GH distribution.
• Markov regime switching model is employed to identify different volatility states.
• NIG model provides a robust and consistently better fit.
• VG model performs poorly as the leptokurtic feature of data is more pronounced.

In this study Variance-Gamma (VG) and Normal-Inverse Gaussian (NIG) distributions are compared with the benchmark of generalized hyperbolic distribution in terms of their fit to the empirical distribution of high-frequency stock market index returns in China. First, we estimate the considered models in a Markov regime switching framework for the identification of different volatility regimes. Second, the goodness-of-fit results are compared at different time scales of log-returns. Third, the goodness-of-fit results are validated through bootstrapping experiments. Our results show that as the time scale of log-returns decrease NIG model outperforms the VG model consistently and the difference between the goodness-of-fit statistics increase. For high-frequency Chinese index returns, NIG model is more robust and provides a better fit to the empirical distributions of returns at different time scales.