Multi-Factor Polynomial Diffusion Models and Inter-Temporal Futures Dynamics

TL;DR

This paper introduces polynomial diffusion models for multi-factor commodity futures, enabling the incorporation of non-linear effects and providing methods for parameter estimation and matrix exponential computation.

Contribution

It develops a novel class of polynomial diffusion models for futures dynamics and compares filtering techniques for latent factor estimation.

Findings

Polynomial diffusion models effectively capture non-linear effects in futures prices.

Filtering methods show varying performance in parameter and latent factor estimation.

Accurate matrix exponential approximation is crucial as polynomial order increases.

Abstract

In stochastic multi-factor commodity models, it is often the case that futures prices are explained by two latent state variables which represent the short and long term stochastic factors. In this work, we develop the family of stochastic models using polynomial diffusion to obtain the unobservable spot price to be used for modelling futures curve dynamics. The polynomial family of diffusion models allows one to incorporate a variety of non-linear, higher-order effects, into a multi-factor stochastic model, which is a generalisation of Schwartz and Smith (2000) two-factor model. Two filtering methods are used for the parameter and the latent factor estimation to address the non-linearity. We provide a comparative analysis of the performance of the estimation procedures. We discuss the parameter identification problem present in the polynomial diffusion case, regardless, the futures prices can still be estimated accurately. Moreover, we study the effects of different methods of calculating matrix exponential in the polynomial diffusion model. As the polynomial order increases, accurately and efficiently approximating the high-dimensional matrix exponential becomes essential in the polynomial diffusion model.