Evaluating Energy Forward Dynamics Modeled as a Subordinated Hilbert-Space Linear Functional

Abstract

In this study, we evaluate energy forward dynamics modeled as time-change Hilbert-space of linear functional. The energy forward is represented as an element of Hilbert-space of function. Representing energy forward and futures contracts as a time-changing stochastic process in a Hilbert-space of functions shows clearly, that an arbitrage-free forward price can be derived from the buy-and hold strategy in the energy market thereby enabling investors in the market willing to be salvage from the market uncertainties as well as Arrow-Debreu situations to execute a spot or forward contracts depending on the time and place the market becomes favorable. With a clock measuring speed of evolution or data frequency for the energy stock market, the distribution of the increments of the Lévy process with the subordinator is subordinated to the distribution of increments of the Lévy process and the results are utilized to price forward contracts of a sample electricity commodity.