Applications of Lévy Semistationary Processes to Storable Commodities

Abstract

Volatility Modulated Lévy-driven Volterra (VMLV) processes have been applied by Barndorff-Nielsen, Benth and Veraart (2013) to construct a new framework for modelling spot prices of non-storable commodities, namely energy. In this thesis, we extend this framework to storable commodities by showing that successful classical models belong to the framework albeit under some parameter restrictions (a result which to our knowledge is new). Additionally, we propose a new model for spot prices of storable commodities which is built on the VMLV processes and their important subclass of so-called Lévy semi-stationary (LSS) processes. The main feature of the framework exploited in the model proposed in this thesis is the memory of the VMLV processes which is used judiciously to account for cumulative changes in inventory over time and the corresponding expected changes in prices and volatility. To the best of our knowledge, this is the first study which uses the LSS processes to investigate pricing in storable (as opposed to non-storable) commodity markets to account for the impact of inventory on pricing. To complement the theoretical development of the new model, we also provide in this thesis a companion set of calibration and empirical analyses to shed light on the new model’s performance compared to previously established models in the literature.