Spot Convenience Yield Models for the Energy Markets

We review that part of the literature on energy spot price models which involves convenience yield as a factor, our goal being to document the shortcomings of the most commonly used models. From a mathematical point of view, the introduction of the convenience yield is usually justified by the desire to reconciliate dynamical models for the time evolution of commodity prices with standard arbitrage theory. Since the convenience yield appears as a factor which cannot be observed directly, stochastic filtering has been proposed as a strategy of choice for its estimation from observed market prices. We implement these ideas on the models we review, and on some natural extensions. We illustrate the inconsistencies of the spot models on readily available data, paving the way for the empirical analysis of models of the term structure of convenience yield recently proposed as a viable alternative.