Question

Calculate the price of a 45-day futures contract, if you know that 45-day call options on the underlying with strike of $268 trade for c=$19.8 and put options with the same maturity and exercise price trade for $16.5. The risk free rate is 1.5%.

Answer 1

Using put call parity we can find the price of the underlying:

C+Xe^-rt=S+P

Where C=call price

             X=strike price

            S= stock price

            P= put price

19.80+268e^{-0.0150*45/360}=S+16.50

=19.80+267.498=S+16.50

=S=270.7980

Therefore, 45 day future price will be:Se^rt

= 270.7980e^{0.0150*(45/360)}

                                                                                 = $ 271.3062