Spot Convenience Yield Models for Energy Assets

As the energy markets continue to evolve, valuation of energy-linked assets has been one of the focal topics of recent finance research. One of the most popular choices for describing asset movements is a class of the so-called ”convenience yield models”. Such models introduce a new unobserved quantity related to physical ownership of the asset. In turn, convenience yield models can be broadly split into ”spot” models and ”term structure factor” models. To the first group belong the classical Gibson and Schwartz model [8], as well as later models of Schwartz [19], Hilliard and Reis [12], and Casassus and Collin-Dufresne [7]. The ”term structure” models, which have been discussed among others by Miltersen and Schwartz [17], and Bjork and Landen [2] are similar to Heath-Jarrow-Morton constructions in fixed income. In this paper we review the literature of spot convenience yield models and analyze two new extensions. First, we discuss a variant of the GibsonSchwartz model with time-dependent parameters. This was first suggested by Miltersen [16], but we provide the first full implementation of the model using empirical data. Second, we describe a new three-factor affine model with stochastic convenience yield and stochastic market price of risk. The existence of a third factor allows us to achieve a good fit to the cross-section of futures prices. The idea of time-dependent risk premia has been recently proposed by Casassus and Collin-Dufresne [7], however, they only consider the deterministic case. We believe that a stochastic version is much more