Multi-Factor Model of Correlated Commodity – Forward Curves for Crude Oil and Shipping Markets
Paul D. Sclavounos and Per Einar Ellefsen
An arbitrage free multi-factor model is developed of the correlated forward curves of the crude oil, gasoline, heating oil and tanker shipping markets. Futures contracts trading on public exchanges are used as the primary underlying securities for the development of a multi-factor Gaussian Heath-Jarrow-Morton (HJM) model for the dynamic evolution of the correlated forward curves. An intra- and inter-commodity Principal Component Analysis (PCA) is carried out in order to isolate seasonality and identify a small number of independent factors driving each commodity market. The cross-commodity correlation of the factors is estimated by a two step PCA. The factor volatilities and cross-commodity factor correlations are studied in order to identify stable parametric models, heteroskedasticity and seasonality in the factor volatilities and correlations. The model leads to explicit stochastic differential equations governing the short term and long term factors driving the price of the spot commodity under the risk neutral measure. Risk premia are absent, consistently with HJM arbitrage free framework, as they are imbedded in the factor volatilities and correlations estimated by the PCA. The use of the model is described for the pricing of derivatives written on inter- and intra-commodity futures spreads, Asian options, the valuation and hedging of energy and shipping assets, the fuel efficient navigation of shipping fleets and use in corporate risk management.