29 Pages Posted: 12 Feb 2008 Last revised: 5 Dec 2008
Date Written: July 22, 2008
Realized volatility is a nonparametric ex-post estimate of the return variation. The most obvious realized volatility measure is the sum of finely-sampled squared return realizations over a fixed time interval. In a frictionless market the estimate achieves consistency for the underlying quadratic return variation when returns are sampled at increasingly higher frequency. We begin with an account of how and why the procedure works in a simplified setting and then extend the discussion to a more general framework. Along the way we clarify how the realized volatility and quadratic return variation relate to the more commonly applied concept of conditional return variance. We then review a set of related and useful notions of return variation along with practical measurement issues (e.g., discretization error and microstructure noise) before briefly touching on the existing empirical applications.
Keywords: Realized Volatility, Stochastic Volatility, Quadratic Variation, Bipower Variation, Variance Swap, Impled Volatility
JEL Classification: G12, G13, C22, C32, C53
Suggested Citation: Suggested Citation