  We examine a general multi-factor model for commodity spot prices and futures
valuation. We extend the multi-factor long-short model in Schwartz and Smith
(2000) and Yan (2002) in two important aspects: firstly we allow for both the
long and short term dynamic factors to be mean reverting incorporating
stochastic volatility factors and secondly we develop an additive structural
seasonality model. Then a Milstein discretized non-linear stochastic volatility
state space representation for the model is developed which allows for futures
and options contracts in the observation equation. We then develop numerical
methodology based on an advanced Sequential Monte Carlo algorithm utilising
Particle Markov chain Monte Carlo to perform calibration of the model jointly
with the filtering of the latent processes for the long-short dynamics and
volatility factors. In this regard we explore and develop a novel methodology
based on an adaptive Rao-Blackwellised version of the Particle Markov chain
Monte Carlo methodology. In doing this we deal accurately with the
non-linearities in the state-space model which are therefore introduced into
the filtering framework. We perform analysis on synthetic and real data for oil
commodities.
