Daily average temperature variations are modelled with a mean-reverting Ornstein-Uhlenbeck process driven by a generalized hyperbolic Levy process and having seasonal mean and volatility. It is empirically demonstrated that the proposed dynamics fits Norwegian temperature data quite...

Arbitrage theory is used to price forward (futures) contracts in energy markets, where the underlying assets are non-tradeable. The method is based on the so-called 'fitting of the yield curve' technique from interest rate theory. The spot price dynamics of Schwartz is generalized to...

Following the increasing awareness of the risk from volatility fluctuations, the market for hedging contracts written on realized volatility has surged. Companies looking for means to secure against unexpected accumulation of market activity can find over-the-counter products written on...

A mean-reverting model is proposed for the spot price dynamics of electricity which includes seasonality of the prices and spikes. The dynamics is a sum of non-Gaussian Ornstein-Uhlenbeck processes with jump processes giving the normal variations and spike behaviour of the prices. The amplitude...

In this paper we provide a framework that explains how the market risk premium, defined as the difference between forward prices and spot forecasts, depends on the risk preferences of market players. In commodities markets this premium is an important indicator of the behaviour of buyers and...

We propose a spatial-temporal stochastic model for daily average surface temperature data. First, we build a model for a single spatial location, independently on the spatial information. The model includes trend, seasonality, and mean reversion, together with a seasonally dependent variance of...

We consider an optimal portfolio-consumption problem which incorporates the notions of durability and intertemporal substitution. The logreturns of the uncertain assets are not necessarily normally distributed. The natural models then involve Lévy processes as driving noise instead of the more...

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...