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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 a new modelling framework for electricity forward markets based on so– called ambit fields. The new model can capture many of the stylised facts observed in energy markets and is highly analytically tractable. We give a detailed account on the probabilistic properties of the new type of model, and we discuss martingale conditions, option… (More)

This paper introduces a new class of stochastic volatility models which allows for stochastic volatility of volatility (SVV): Volatility modulated non–Gaussian Ornstein–Uhlenbeck (VMOU) processes. Various probabilistic properties of (integrated) VMOU processes are presented. Further we study the effect of the SVV on the leverage effect and on the presence… (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)

This paper introduces the concept of stochastic volatility of volatility in continuous time and, hence, extends standard stochastic volatility (SV) models to allow for an additional source of randomness associated with greater variability in the data. We discuss how stochastic volatility of volatility can be defined both non–parametrically, where we link it… (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)

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

This paper introduces a new class of stochastic volatility models which allows for stochastic volatility of volatility. Such models are given by volatility modulated non–Gaussian Ornstein Uhlenbeck processes. We study the probabilistic properties of such models both under the physical and under the risk neutral probability measure, where we focus in… (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)

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)

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