Realised Power Variation and Stochastic Volatility Models

Abstract

Limit distribution results on realised power variation, that is sums of absolute powers of increments of a process, are derived for certain types of semimartingale with continuous local martingale component, in particular for a class of flexible stochastic volatility models. The theory covers, for example, the cases of realised volatility and realised absolute variation. Such results should be helpful in, for example, the analysis of volatility models using high frequency information.

Keywords: Absolute returns, Mixed asymptotic normality, Realised volatility, p-variation, Quadratic variation