Higher-Order Volatility: Dynamics and Sensitivities

Higher-Order Volatility: Time Series

“…Here we recall some basic definitions and results from Carey (2005Carey ( , 2006. Let X t ( ) be a positive-valued adapted stochastic process on a filtered probability space !, F , F t ( ),Q ( ) , t !…”

“…X t ( ) derivation. This formula and a related one were originally obtained in Carey (2005Carey ( , 2006 under the assumption that the finite-period volatilities are deterministic for very small time horizons !t . While not as clean as the assumption we make above, it perhaps carries more intuition.…”