This paper reviews the roles of gamma type kernels in the theory and modelling for Brownian and Lévy semistationary processes. Applications to financial econometrics and the physics of turbulence are pointed out.

This paper reviews and puts in context some of our recent work on stochastic volatility (SV) modelling for financial economics. Here our main focus is on: (i) the relationship between subordination and SV, (ii) OU based volatility models, (iii) exact option pricing, (iv) realized power...

This paper looks at some recent work on estimating quadratic variation using realized variance (RV) - that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high-frequency financial return data. When the underlying process is a...

Non-Gaussian processes of Ornstein–Uhlenbeck (OU) type offer the possibility of capturing important distributional deviations from Gaussianity and for flexible modelling of dependence structures. This paper develops this potential, drawing on and extending powerful results from probability...

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...