Suppose that the futures price of a commodity is 500 cents, the strike price of

Question

Suppose that the futures price of a commodity is 500 cents, the strike price of a futures option is 550 cents, the risk-free rate of interest is 3%, the volatility of the futures price is 20%, and the time to maturity of the option is 9 months

a. What is the price of the option if it is a European call?

b. What is the price of the option if it is a European put?

c. Verify that put-call parity holds

d. What is the futures price for a futures style option if it is a call?

e. What is the futures price for a futures style option if it is a put?

Explanation / Answer

A) the value of a European call option >= Max {(s-x)/(1+r)^t , 0 }.........which means >= 0 .................. B) the value of a European put option >= Max { x/(1+r)^t - S , 0 }........which means >= Max {37.9412 , 0 } .... or > = 37.9412 cents............... C) the call put parity holds as it can be seen from part A and part B the minimum price of the call option is less than the minimum possible price of the put option........... D) the futures price of a futures style option if it is a call can be anywhere between 0 and (underlying price - exercise price) if it is an American call Option and the formula used in part A) above if it is a European call Option............. E) the futures price of a futures style option if it is a put can be anywhere between 0 and (exercise price - underlying price) if it is an American put option or the formula used above in part B) if it is a European put option................

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