Realized Volatility and Multipower Variation

Abstract

This article 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 article discusses applications of these measures for reduced‐form volatility modeling and forecasting as well as testing for the presence of jumps.

Asymmetric volatility spillovers and consumption risk-sharing

“…Consider the traditional realized volatility (RV) estimator, as explained for example in Andersen and Todorov (2010). The RV estimator of log asset prices 𝑌 can be expressed as:…”

Noise recovery for Lévy-driven CARMA processes and high-frequency behaviour of approximating Riemann sums

“…The constantly increasing availability of high-frequency data in finance and sciences in general has sparked in the last decade a great deal of attention about the asymptotic behaviour of highfrequency sampled processes, especially concerning the estimation of multi-power variations of Itō semimartingales (see, e.g., Andersen and Todorov (2010), Barndorff-Nielsen and Shephard (2003)), employing their realised counterparts. These quantities are of primary importance to practitioners, since they embody the deviation of data from a Brownian motion.…”