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Abstract: Long-term forward contract markets are established in several basic commodities, such as crude oil and copper, and have been modelled by several authors using multi-factor models. We review the two- and three-factor stochastic models for forward crude oil and the closed form solutions, and provide solutions for some additional multi-factor models. We believe these additional models reflect the dynamics of the time series of oil prices. Then we derive the "implied parameters" for all of the... (Update)
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Our innovations are: providing closed-form solutions to some interesting and relevant multi-factor models, deriving the implied parameters over a sample period, and testing model effectiveness by the time varying errors. We believe this methodology provides several interesting insights into the valuation and effectiveness of long-term forward contracts.Citations (may not include all citations):
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