Derivatives Pricing in Energy Markets: An Infinite-Dimensional Approach

Abstract

Based on forward curves modelled as Hilbert-space valued processes, we analyze the pricing of various options relevant in energy markets. In particular, we connect empirical evidence about energy forward prices known from the literature to propose stochastic models. Forward prices can be represented as linear functions on a Hilbert space, and options can thus be viewed as derivatives on the whole curve. The value of these options are computed under various specifications, in addition to their deltas. In a second part, cross-commodity models are investigated, leading to a study of square integrable random variables with values in a two-dimensional Hilbert space. We analyze the covariance operator and representations of such variables, as well as presenting applications to the pricing of spread and energy quanto options.