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

Victor Alexander Okhuese,Joseph Mung’Atu,Jane Akinyi Aduda

doi:10.4236/jmf.2020.103025

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.

Highlights

The forward pricing dynamics of an incomplete Arrow Debreu world reveals interesting challenges to speculators and one such challenge is the stochastic nature of the return process for every investment in an underlying commodity stock
We evaluate energy forward dynamics modeled as time-change Hilbert-space of linear functional
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

Summary

Introduction

The forward pricing dynamics of an incomplete Arrow Debreu world reveals interesting challenges to speculators and one such challenge is the stochastic nature of the return process for every investment in an underlying commodity stock. We adopt the completeness properties of a Banach space (a special type of Hilbert space) such that the return process X (t ) is defined in some normed space (i.e. complete, without hole) to enable us capture all discrete moving forward rates in the corresponding forward curves of the pricing dynamics, as such adopting similar approach by [1] and [2]. This approach is considered such that the distance between two nodes defined by the daily change price on the curve is defined in norm spaces with no gap in the sequence Xt , Xt+1, Xt+2 , , Xt+n , where n = 1, 2, 3, with each representing a node in a forward curve of the energy forward contracts. In literature ([4] [6] [7] and [8]), it is clear that the fundamental relationship between the spot and forward is highly delicate in energy markets and it is only fair to model the forward price dynamics directly

Characteristics Function of a Subordinated Lévy Process

Stochastic Integrals of a Subordinated Lévy Process in Hilbert Space

Evaluating Energy Forward Dynamics as a Subordinated Hilbert Space

Estimation of Forward Prices with and without Lévy Jump

Conclusion and Suggestions

Primary Contribution