arXiv subjects

Almut E. D. Veraart

Publications and source records attributed to Almut E. D. Veraart.

40 records · Page 3Linked to original sources

arXiv2014

Stationary and multi-self-similar random fields with stochastic volatility

This paper introduces stationary and multi-self-similar random fields which account for stochastic volatility and have type G marginal law. The stationary random fields are constructed using volatility modulated mixed moving average fields and their probabilistic properties are discussed. Also, two methods for parameterising the weight functions in the moving average representation are presented: One method is based on Fourier techniques and aims at reproducing a given correlation structure, the other method is based on ideas from stochastic partial differential equations. Moreover, using a generalised Lamperti transform we construct volatility modulated multi-self-similar random fields which have type G distribution.

math.PR↗

arXiv2013

Modelling energy spot prices by volatility modulated Lévy-driven Volterra processes

This paper introduces the class of volatility modulated Lévy-driven Volterra (VMLV) processes and their important subclass of Lévy semistationary (LSS) processes as a new framework for modelling energy spot prices. The main modelling idea consists of four principles: First, deseasonalised spot prices can be modelled directly in stationarity. Second, stochastic volatility is regarded as a key factor for modelling energy spot prices. Third, the model allows for the possibility of jumps and extreme spikes and, lastly, it features great flexibility in terms of modelling the autocorrelation structure and the Samuelson effect. We provide a detailed analysis of the probabilistic properties of VMLV processes and show how they can capture many stylised facts of energy markets. Further, we derive forward prices based on our new spot price models and discuss option pricing. An empirical example based on electricity spot prices from the European Energy Exchange confirms the practical relevance of our new modelling framework.

q-fin.PR↗

arXiv2012

Recent advances in ambit stochastics with a view towards tempo-spatial stochastic volatility/intermittency

Ambit stochastics is the name for the theory and applications of ambit fields and ambit processes and constitutes a new research area in stochastics for tempo-spatial phenomena. This paper gives an overview of the main findings in ambit stochastics up to date and establishes new results on general properties of ambit fields. Moreover, it develops the concept of tempo-spatial stochastic volatility/intermittency within ambit fields. Various types of volatility modulation ranging from stochastic scaling of the amplitude, to stochastic time change and extended subordination of random measures and to probability and Lévy mixing of volatility/intensity parameters will be developed. Important examples for concrete model specifications within the class of ambit fields are given.

math.PR↗

arXiv2012

On stochastic integration for volatility modulated Lévy-driven Volterra processes

This papers develops a stochastic integration theory with respect to volatility modulated Lévy-driven Volterra (VMLV) processes. It extends recent results in the literature to allow for stochastic volatility and pure jump processes in the integrator. The new integration operator is based on Malliavin calculus and describes an anticipative integral. Fundamental properties of the integral are derived and important applications are given.

math.PR↗