Realized Volatility and Multipower Variation

This paper reviews basic notions of return variation in the context of a continuous-time arbitrage-free asset pricing model and discusses some of their applications. We first define return variation in the infeasible continuous-sampling case. Then we introduce realized measures obtained from high-frequency observations which provide consistent and asymptotically normal estimates of the underlying return variation. The paper discusses applications of these measures for reduced-form volatility modeling and forecasting as well as testing for the presence of jumps.