We develop a novel class of time-changed Lévy models which are tractable and readily applicable, capture the leverage effect, and exhibit pure jump processes with finite or infinite activity. Our models feature four nested processes reflecting market, volatility and jump risks, and observation...

In this paper we consider two processes driven by Brownian motions plus drift and jumps with infinite activity. Given discrete observations on a finite time horizon, we study the truncated (threshold) realized covariance \hat{IC} to estimate the integrated covariation IC between the two Brownian...