What is the no arbitrage price differential

Problem: 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 expires exactly six month from now:

Exercise price    Put price    Call Price
40    0.59    8.73
45    1.93    0
50    0    2.47

1) 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.

2) 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 arbitrage trade to take advantage of the mispricing.

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