We consider the construction of normal inverse Gaussian (NIG) (and some related) Levy processes from the probabilistic viewpoint and from that of the theory of pseudo-differential operators; we then introduce and analyse natural generalizations of these constructions. The resulting Feller...

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...

Motivated by features of low latency data in financial econometrics we study in detail integer-valued Lévy processes as the basis of price processes for high-frequency econometrics. We propose using models built out of the difference of two subordinators. We apply these models in practice to...