Multi-factor polynomial diffusion models and inter-temporal futures dynamics

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review


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 multifactor stochastic model, which is a generalisation of Schwartz and Smith [17] twofactor 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.
Original languageEnglish
Title of host publication2021-2022 MATRIX Annals
EditorsDavid R. Wood, Jan de Gier, Cheryl E. Praeger
Place of PublicationCham
PublisherSpringer, Springer Nature
ISBN (Electronic)9783031474170
ISBN (Print)9783031474194, 9783031474163
Publication statusAccepted/In press - 20 Jun 2023

Publication series

NameMATRIX Book Series
ISSN (Print)2523-3041


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