Derivatives pricing in energy markets: an infinite dimensional approach

TL;DR

This paper develops an infinite-dimensional Hilbert space framework for energy derivatives pricing, connecting empirical forward price data to stochastic models and extending to cross-commodity options.

Contribution

It introduces a novel Hilbert space approach for modeling energy forward curves and options, including cross-commodity derivatives, with explicit valuation and sensitivity analysis.

Findings

Representation of forward prices as linear functions in Hilbert space

Pricing formulas for energy options and their deltas

Analysis of covariance operators for cross-commodity models

Abstract

Based on forward curves modelled as Hilbert-space valued processes, we analyse 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 analyse the covariance operator and representations of such variables, as well as presenting applications to pricing of spread and energy quanto options.