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Futures and Options

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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

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 arbitrage trade to take advantage of the mispricing.

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

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.

Put option
For no arbitrage
At time t= 0
Buy a 6 - month put optiont with an exercise price of $50.00 for $X
Enter into a long position on the 6 month futures contract to purchase the commodity at $48.00
Cash outflow at time t= 0 is $X
(Since there is no payment on the futures contract at the initiation of the contract)

At time t= 6 months

Use the futures contract to purchase the commodity at $48.00
Use the put option to sell the commodity at $50.00
Cash inflow at time t= 6 months = $2.00 =50-48

For no arbitrage we equate the present value of ...

Solution Summary

Calculates the price of the put and call options using no arbitrage conditions.

$2.19