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The availability of intra-day data on the prices of speculative assets means that we can use quadratic variation like measures of activity in financial markets, called realised volatility , to study the stochastic properties of returns. Here, under the assumption of a rather general stochastic volatility model, we derive the moments and the asymptotic… (More)

This paper shows that realised power variation and its extension called realised bipower variation that we introduce here is somewhat robust to rare jumps. We demonstrate that in special cases realised bipower variation estimate integrated variance in stochastic volatility models, thus providing a model free and consistent alternative to realised variance.… (More)

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 from probability theory for applications in statistical… (More)

- Ole E. Barndorff-Nielsen
- Finance and Stochastics
- 1997

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 also apply the tests to exchange rate data and show that the null… (More)

This paper analyses multivariate high frequency financial data using realised covariation. We provide a new asymptotic distribution theory for standard methods such as regression, correlation analysis and covariance. It will be based on a fixed interval of time (e.g. a day or week), allowing the number of high frequency returns during this period to go to… (More)

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 semimartingale we recall the fundamental result that RV is a… (More)

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, for example, the cases of realised volatility and realised… (More)

We propose a multivariate realised kernel to estimate the ex-post covariation of log-prices. We show this new consistent estimator is guaranteed to be positive semi-definite and is robust to measurement noise of certain types and can also handle non-synchronous trading. It is the first estimator which has these three properties which are all essential for… (More)

This paper discusses two classes of distributions, and stochastic processes derived from them: modified stable (MS) laws and normal modified stable (NMS) laws. This extends corresponding results for the generalised inverse Gaussian (GIG) and generalised hyperbolic (GH) or normal generalised inverse Gaussian (NGIG) laws. The wider framework thus established… (More)