On the Parameter Estimation in the Schwartz-Smiths Two-Factor Model

TL;DR

This paper develops a Kalman Filter-based approach to jointly estimate unobservable short and long-term factors in the Schwartz-Smith two-factor model, addressing parameter identification issues and validating the method with simulated data.

Contribution

It introduces a new constraint to improve parameter estimation within the Kalman Filter framework for the Schwartz-Smith model.

Findings

Conditional MLEs are consistent within the KF framework

The methodology performs well on simulated data

Parameter estimation accuracy is improved by the proposed constraint

Abstract

The two unobservable state variables representing the short and long term factors introduced by Schwartz and Smith in [16] for risk-neutral pricing of futures contracts are modelled as two correlated Ornstein-Uhlenbeck processes. The Kalman Filter (KF) method has been implemented to estimate the short and long term factors jointly with un- known model parameters. The parameter identification problem arising within the likelihood function in the KF has been addressed by introduc- ing an additional constraint. The obtained model parameter estimates are the conditional Maximum Likelihood Estimators (MLEs) evaluated within the KF. Consistency of the conditional MLEs is studied. The methodology has been tested on simulated data.