Consider Commodity Z, which has both exchange-traded futures and option contracts associated with it. As you look in today€™s paper, you find the following put and call prices for options that expire exactly six months from now:

a. Assuming that the futures price of a six-month contract on Commodity Z is $48, what must be the price of a put with an exercise price of $50 in order to avoid arbitrage across markets? Similarly, calculate the "no arbitrage" price of a call with an exercise price of $45. In both calculations, assume that the yield curve is flat and the annual risk-free rate is 6 percent.
b. What is the "no arbitrage" price differential that should exist between the put and call options having an exercise price of $40? Is this differential satisfied by current market prices? If not, demonstrate an arbitrage trade to take advantage of themispricing.

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Exercise Price 40 45 50 Put Price $0.59 1.93 Call Price $8.73 2.47