volatility price processes are now the main tools in modern dynamic asset pricing theory. In this paper, we introduce the theory … returns. We apply the proposed models to modeling S&P 500 returns, treating the CBOE Volatility Index as intrinsic time change … and the CBOE Volatility-of-Volatility Index as the volatility subordinator. We find that these volatility indexes are not …

volatility, volatility-of-volatility, and Merton-jump diffusion are derived …