Schwartz-Smith Model

Multi-Factor Function-on-Function Regression of Bond Yields on WTI Commodity Futures Term Structure Dynamics ArXiv ID: 2412.05889 “View on arXiv” Authors: Unknown Abstract In the analysis of commodity futures, it is commonly assumed that futures prices are driven by two latent factors: short-term fluctuations and long-term equilibrium price levels. In this study, we extend this framework by introducing a novel state-space functional regression model that incorporates yield curve dynamics. Our model offers a distinct advantage in capturing the interdependencies between commodity futures and the yield curve. Through a comprehensive empirical analysis of WTI crude oil futures, using US Treasury yields as a functional predictor, we demonstrate the superior accuracy of the functional regression model compared to the Schwartz-Smith two-factor model, particularly in estimating the short-end of the futures curve. Additionally, we conduct a stress testing analysis to examine the impact of both temporary and permanent shocks to US Treasury yields on futures price estimation. ...

Multi-Factor Polynomial Diffusion Models and Inter-Temporal Futures Dynamics ArXiv ID: 2409.19386 “View on arXiv” Authors: Unknown 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. ...

PDSim: A Shiny App for Simulating and Estimating Polynomial Diffusion Models in Commodity Futures ArXiv ID: 2409.19385 “View on arXiv” Authors: Unknown Abstract PDSim is an R package that enables users to simulate commodity futures prices using the polynomial diffusion model introduced in Filipovic & Larsson (2016) through both a Shiny web application and R scripts. For user-supplied data, a standalone R routine has been developed to provide joint estimation of state variables and model parameters via the Extended Kalman Filter (EKF) or Unscented Kalman Filter (UKF). With its user-friendly interface, PDSim makes the features of simulations and estimations accessible. To date, it is the only package specifically designed for the simulation and estimation of the polynomial diffusion model. The Schwartz-Smith two-factor model (Schwartz & Smith, 2000) is also available within this package for both simulation and calibration. The package is validated through several tests, including replication of the results in Schwartz & Smith (2000), unit testing of the coverage rate, and verification of the outputs of the main functions. ...