In order to assess the effect of jumps on realised variance calculations, we study some of the econometric properties of time-changed Lévy processes. We show that in general realised variance is an inconsistent estimator of the time-change, however we can derive the second order properties of realised variances and use these to estimate the parameters of such models. Our analytic results give a first indication of the degrees of inconsistency of realised variance as an estimator of the time-change in the non-Brownian case. Further, our results suggest volatility is even more predictable than has been shown by the recent econometric work on realised variance.
Finally, and closest to this paper, REF have studied the second order properties of realised variance under the assumption that the local martingale component of prices is a time-changed Lévy process.
Impact of Jumps on Returns and Realised Variances: Econometric analysis of time-deformed Lévy processes
Journal of Econometrics
Economics Mathematics