Explore BrainMass
Share

Explore BrainMass

    Futures and Options

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com October 9, 2019, 10:25 pm ad1c9bdddf
    https://brainmass.com/business/options/futures-and-options-219676

    Solution Preview

    Please see attached file

    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