Modelling energy spot prices by volatility modulated L\'{e}vy-driven Volterra processes

TL;DR

This paper introduces a new class of stochastic processes called VMLV processes for modeling energy spot prices, capturing features like jumps, spikes, and autocorrelation, with practical applications demonstrated through empirical data.

Contribution

The paper develops the VMLV process framework, integrating stochastic volatility and jump features, and applies it to energy markets for improved modeling and pricing.

Findings

VMLV processes effectively model stylized facts of energy prices.

The framework allows for flexible autocorrelation and Samuelson effects.

Empirical analysis confirms the model's practical relevance.

Abstract

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, 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.