Calibration And Filtering For Multi Factor Commodity Models With Seasonality: Incorporating Panel Data From Futures Contracts
The authors examine a general multi-factor model for commodity spot prices and futures valuation. They extend the multi-factor long-short model in and in two important aspects: firstly, they allow for both the long and short term dynamic factors to be mean reverting incorporating stochastic volatility factors and secondly, they 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. They 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.