Gamma Energy is an oil producing company that owns an oil field from which it can deliver 10 mln barrels of oil per year for the next four years. The current oil price is USD 75 per barrel. Extraction costs are currently USD 60 per barrel.

Storage costs for oil are 2% per barrel (continuously compounded), and the (continuously compounded) interest rates for maturities of 1, 2, 3, and 4 years are 1.50%, 1.75%, 2.00% and 2.40% respectively. The convenience yields for oil for maturities of 1 up to 4 years are 4.0%, 2.0%, 1.0% and 0.5% (annually) respectively.

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1. If Gamma wants to hedge its oil price risk with oil forwards (or futures), what would be the theoretical forward (futures) prices? What would be the gross margin that Gamma could lock in?

2. If storage costs would be USD 2 per barrel instead of 2%, what would be the theoretical forward (futures) prices?

3. (Assume storage costs of 2% again.) If Gamma wants to hedge its oil price risk with a swap contract, what could the contract look like? What would be the theoretical swap price?

4. How could Gamma hedge its risk with one-year forwards (or futures) in a stack-and-roll hedge?

It is currently 1 January 2018. Gamma is supposed to deliver the oil to its customers every year (2018 – 2021) only at year end, 31 December. Its productions facilities allow Gamma to produce (pump) the oil within a matter of weeks.

5. How could Gamma benefit from the convenience yield in the oil forwards (futures)? What would be the additional profit compared to physical delivery?