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.

Ignoring storage costs for oil, assuming volatility of the oil price is 20% 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.

1. If Gamma wants to hedge the downside of its exposure, but remain the upside, what plain vanilla options could it use? What would be the theoretical price of the options?

Gamma has as a policy that once the oil price falls below USD 60 (production costs), it will stop producing.

2. If this is the policy, and Gamma wants to hedge its risk with options, what exotic options would you recommend. What would be the price of these options?

3. Gamma wants to insure itself against oil prices below USD 75, but needs this to be effective only when the oil price falls below USD 60. What option do you suggest and what would be the price of these options?

Gamma beliefs that once the oil price exceeds USD 100, it will not fall below USD 75 again, and there is no need for a hedge.

4. If this belief is correct, what exotic option would you suggest to Gamma, and what would be the price?

Gamma is exposed to the oil price at the end of each of the coming four years.

5. Suppose it wants to hedge itself with an option on the average of those four oil prices against the current price of USD 75 (the exercise price). What is the price of this option?