Approximation of forward curve models in commodity markets with arbitrage-free finite dimensional models

TL;DR

This paper develops a method to approximate complex forward curve models in commodity markets with simpler, finite-dimensional, arbitrage-free models, providing explicit formulas and convergence rates.

Contribution

It introduces a novel approach using Riesz bases to construct finite-dimensional, arbitrage-free approximations of Heath-Jarrow-Morton models for commodity forward prices.

Findings

Explicit closed-form representations of approximate models

Uniform convergence rates over time to the true dynamics

Enhanced convergence in the Markovian case

Abstract

In this paper we show how to approximate a Heath-Jarrow-Morton dynamics for the forward prices in commodity markets with arbitrage-free models which have a finite dimensional state space. Moreover, we recover a closed form representation of the forward price dynamics in the approximation models and derive the rate of convergence uniformly over an interval of time to maturity to the true dynamics under certain additional smoothness conditions. In the Markovian case we can strengthen the convergence to be uniform over time as well. Our results are based on the construction of a convenient Riesz basis on the state space of the term structure dynamics.