This paper provides limit distribution results for power variation, that is sums of powers of absolute increments, for certain types of time-changed Brownian motion and $alpha $-stable processes. Special cases of these processes are stochastic volatility models used extensively in financial...

Limit distribution results on realised power variation, that is sums of absolute powers of increments of a process, are derived for certain types of semimartingale with continuous local martingale component, in particular for a class of flexible stochastic volatility models. The theory covers,...

This is a draft Chapter from a book by the authors on “Levy Driven Volatility Modelsâ€.

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

Non-Gaussian processes of Ornstein-Uhlenbeck type, or OU processes for short, 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...

In this paper we will rigorously study some of the properties of continuous time stochastic volatility models. We have five main results: (i) the stochastic volatility class can be linked to Cox process based models of tick-by-tick financial data; (ii) we characterise the moments, autocorrelation...

In this note we show how the stochastic volatility model of Barndorff-Nielsen and Shephard (1998a) can be generalised to allow for the leverage effect. That is where a negative return sequence is associated with increases in volatility. This is important in empirical work on stock returns. This...

This paper reviews some recent work in which Levy processes are used to model and analyse time series from financial econometrics. A main feature of the paper is the use of positive Ornstein-Unlenbeck (OU) type processes inside stochastic volatility processes. The basic probability theory...

This paper shows that realised power variation and its extension we introduce here called realised bipower variation is somewhat robust to rare jumps. We show realised bipower variation estimates integrated variance in SV models --- thus providing a model free and consistent alternative to...