We derive an arbitrage-free pricing dynamics for claims on temperature, where the temperature follows a fractional Ornstein-Uhlenbeck process. Using a fractional white noise calculus, one can express the dynamics as a special type of conditional expectation not coinciding with the classical one....

This paper introduces the class of volatility modulated L\'{e}vy-driven Volterra (VMLV) processes and their important subclass of L\'{e}vy semistationary (LSS) processes as a new framework for modelling energy spot prices. The main modelling idea consists of four principles: First,...

In electricity markets, it is sensible to use a two-factor model with mean reversion for spot prices. One of the factors is an Ornstein-Uhlenbeck (OU) process driven by a Brownian motion and accounts for the small variations. The other factor is an OU process driven by a pure jump L\'evy process...

We consider portfolio optimization in futures markets. We model the entire futures price curve at once as a solution of a stochastic partial differential equation. The agents objective is to maximize her utility from the final wealth when investing in futures contracts. We study a class of...

We extend the concept of half life of an Ornstein–Uhlenbeck process to Lévy-driven continuous-time autoregressive moving average processes with stochastic volatility. The half life becomes state dependent, and we analyze its properties in terms of the characteristics of the process. An...

This paper develops a stochastic integration theory with respect to volatility modulated Lévy-driven Volterra (V MLV) 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...

In this paper we study the approximation of a sum of assets having marginal log-returns being multivariate normal inverse Gaussian distributed. We analyse the choice of a univariate exponential NIG distribution, where the approximation is based on matching of moments. Probability densities and...

Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection...

This paper introduces a new modelling framework for energy spot prices based on Lévy semistationary processes. Lévy semistationary processes are special cases of the general class of ambit processes. We provide a detailed analysis of the probabilistic properties of such models and we show how...

In this paper we propose an ARMA time-series model for the wind speed at a single spatial location, and estimate it on in-sample data recorded in three different wind farm regions in New York state. The data have a three-hour granularity, but based on applications to financial wind derivatives...