This paper looks at some recent work on estimating quadratic variation using realised 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...

In this paper we study the reliability of the mixed normal asymptotic distribution of realised variance error, which we have previously derived using the theory of realised power variation. Our experiments suggest that the asymptotics is reliable when we work with the logarithmic transform of...

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...