# Futures and Options

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.