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The mathematical concept of time–changing continuous–time stochastic processes can be regarded as one of the standard tools for building financial models. This article reviews briefly the theory on time–changed stochastic processes and relates them to stochastic volatility models in finance. Popular models, including time–changed Lévy processes, where the… (More)

This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic treatment of stochastic leverage and propose to model the stochastic… (More)

- Andrea Granelli, Almut E. D. Veraart
- SIAM J. Financial Math.
- 2016

This paper introduces a new continuous-time framework for modelling serially correlated count and integer-valued data. The key component in our new model is the class of integer-valued trawl (IVT) processes, which are serially correlated, stationary, infinitely divisible processes. We analyse the probabilistic properties of such processes in detail and, in… (More)

This paper studies the effect of jumps and leverage type effects on return and realised variance calculations when the logarithmic asset price is given by a scaled Lévy processes. In such a model, the realised variance is an inconsistent estimator of the integrated variance. Nevertheless it can be used within a quasi–maximumlikelihood setup to draw… (More)

Here we assume that the logarithmic asset price is given by a semimartingale. Jacod (2006) has derived an infeasible central limit theorem for the realised variance in such a general framework. However, here we focus on constructing a feasible limit theorem. We propose a new estimator for the asymptotic variance of the realised variance. This new estimator… (More)

- Fred E. Benth, Heidar Eyjolfsson, Almut E. D. Veraart
- SIAM J. Financial Math.
- 2014

The present paper discusses simulation of Lévy semistationary (LSS) processes in the context of power markets. A disadvantage of applying numerical integration to obtain trajectories of LSS processes is that such a scheme is not iterative. We address this problem by introducing and analyzing a Fourier simulation scheme for obtaining trajectories of these… (More)

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