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:Exercise PricePut PriceCall Price $          40.00 $             0.59 $             8.73 $          45.00 $             1.93 $                 -   $          50.00 $                 -   $             2.47a. Assuming that the futures price of a six-month contract on Commodity Z is Fo, 0.5 = $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 the mispricing.

Question
Asked Apr 28, 2019
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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 expire exactly six months from now:
Exercise Price Put Price Call Price
 $          40.00  $             0.59  $             8.73
 $          45.00  $             1.93  $                 -  
 $          50.00  $                 -    $             2.47
a. Assuming that the futures price of a six-month contract on Commodity Z is Fo, 0.5 = $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 the mispricing.
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Expert Answer

Step 1

There is a specific relationship that exists between the call premium  and the put premium for an underlying futures contract with the same strike price, same time to expiry and the same underlying futures contract. 

The stated condition must hold at all times. This is also known as the no artibitrage condition.

Any deviation form the put call parity will provide traders with an arbitrage opportunity.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Step 2

 

We  first calculate the price of the put option .

We have : 

Stirke Price (X) =$50

Futures Price (S) : $48

Call Price (C) : $2.47

Annual risk free interest Rate = 6%

Futures Contract Expiry = 6 months

 

Step 3

                                                      

        &nb...

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