I'm dealing with the calibration of the forward curve for energy products. I found an approach proposed by Benth et al., in which the forward curve is parameterized as $f(t) = s(t) + \epsilon(t)$ where $s$ is the seasonality and $\epsilon$ is a smooth curve used to quantify the deviation from the seasonality. In the paper, $s$ has been chosen according to Lucia and Schwartz.

My questions are:

  1. Which alternatives to Benth et al. are used?
  2. Do exist other models other than Lucia and Schwartz for the deterministic function $s$ useful in this setting?
  • $\begingroup$ Is Gabillon model a two factor or one factor model? $\endgroup$
    – Roy Tang
    Commented Oct 3, 2023 at 13:36
  • $\begingroup$ Gabillon: "In this paper, we present a two-variable model of the term structures of futures prices and volatilities assuming that the spot and long-term prices of oil are stochastic, and are the main determinants of the convenience yield function." So yes it is 2 factor even though he does not use the term "factor". $\endgroup$
    – nbbo2
    Commented Oct 3, 2023 at 14:50

1 Answer 1


To answer your first question, an alternative approach is the Gabillion two-factor model (which was originally proposed for oil futures). At a high-level, Gabillon models the spot price as a single-factor Gaussian process that means reverts to a lognormal long-term rate. See here for additional details.


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