In this paper we provide a systematic study of the robustness of probability limits and central limit theory for realised multipower variation when we add finite activity and infinite activity jump processes to an underlying Brownian semimartingale.

Kim, Shephard, and Chib (1998) provided a Bayesian analysis of stochastic volatility models based on a fast and reliable Markov chain Monte Carlo (MCMC) algorithm. Their method rules out the leverage effect, which is known to be important in applications. Despite this, their basic method has...

Limit distribution results on quadratic and higher order variation quantities are derived for certain types of continuous local martingales, in particular for a class of OU-based stochastic volatility models.

In this paper we introduce a decomposition of the joint distribution of price changes of assets recorded trade-by-trade. Our decomposition means that we can model the dynamics of price changes using quite simple and interpretable models which are easily extended in a great number of directions,...

In this paper we provide an asymptotic distribution theory for some non-parametric tests of the hypothesis that asset prices have continuous sample paths. We study the behaviour of the tests using simulated data and see that certain versions of the tests have good finite sample behaviour. We...

GARCH models are commonly used as latent processes in econometrics, financial economics and macroeconomics. Yet no exact likelihood analysis of these models has been provided so far. In this paper we outline the issues and suggest a Markov chain Monte Carlo algorithm which allows the calculation...

We consider kernel-based estimators of integrated variances in the presence of independent market microstructure effects. We derive the bias and variance properties for all regular kernel-based estimators and derive a lower bound for their asymptotic variance. Further we show that the...

In this brief note we review some of our recent results on the use of high frequency financial data to estimate objects like integrated variance in stochastic volatility models. Interesting issues include multipower variation, jumps and market microstructure effects.

In this note we show that the feasible central limit theory for realised volatility and realised covariation recently developed by Barndorff-Nielsen and Shephard applies under arbitrary diffusion based leverage effects. Results from a simulation experiment suggest that the feasible version of...