Question

The current spot price of crude oil is S= $50 per barrel. A US-Refinery called BigOil wants to fix a maximum price at $60 per barrel and a minimum price of $45 per barrel (ignoring any cost of options) that it will pay for 10,000 barrels of crude oil in one years time (T=1). At T, BigOil will purchase its crude oil (from Exxon) in the spot oil market. Appropriate call and put premia are C=$2 and P=$3. a). Explain how it might achieve the above outcome using options on crude oil. Explain the potential outcomes in one year’s time if ST =30 or ST = 50 or ST =70 by drawing the payoff diagram and presenting your results in a table of possible outcomes where: ST < Kp (= 45) ( Kp =) 45 < ST < 60 (= Kc ) ST > Kc =60 In your table include the cost of the (spot) oil, the payoff to the options, the cost of the options and hence the net purchase cost (“effective cost”) of the oil (at T), for BigOil. b). A zero-cost collar has C=P. Briefly explain the steps in constructing a zero-cost collar and any limitations such a strategy entails. Explain whether a zero-cost collar gives you “something for nothing”.

Answer 1

a]

The outcome can be achieved by selling a $45 put and buying a $60 call.

Payoff of a long call option = Max[S-X, 0]

Payoff of a short put option = -Max[0, X-S]

S = underlying price at expiry,

X = strike price

Cost of options = premium paid to buy $60 call - premium received from selling $45 put

Cost of options = $2 - $3 = -$1

Effective cost = spot cost of oil at expiry - total options payoff + cost of options

The results table is below :

The formulas are below :

The graph is below :

b]

In a zero-cost collar, a call option is bought and a put option is sold such that the premium paid to buy the call option equals the premium received on the put option.

The limitation of such a strategy is that if the spot price of oil falls below the strike price of the put, the downside benefit of a lower effective cost is foregone as the losses on the put option will offset the lower spot price of oil.

Yes, a zero cost collar gives you something for nothing. The cost of a zero cost collar is zero (nothing) and gives you the benefit of locking in the effective purchase price within a certain range (something).