Question

Facebook (FB) currently trades at $210.00. You purchase a 23 month European $11.00 strike call option on a short futures contract on one share of FB. The futures delivery date is 43 months from now and the delivery price is $246.00. The risk-free rate is 4.2%. Compute the range of prices of FB 23 months from now that will make you want to exercise your option.

Answer 1

The short futures contract becomes deliverable after 43 months at a price of $246. Its intrinsic value after 23 months can be obtained by discounting the deliverable price for 20 months(F₁) = F₀e^-rt Here F=$246, r= 4.2%/12 = 0.35% monthly rate, t= 20

We get F₁ = The intrinsic value of the contract after 23 months with 20 months left to expire = $229.3689

This is a short futures contract which means the holder stands to profit if the actual price of FB is less than the intrinsic future price because he would be selling it at a price higher than the market price . The difference being the net profit. Thus, the contract is worth the difference between FB market price after 20 months and $229.3689. A call option on such a contract has a strike price of $11  which means the option is in-the-money if contract is worth more than $11 . Contract is worth more than $11 when FB market price is below $(229.3689 -11) = $218.3689. So, the option holder could exercise when FB price is below $218.3689 after 20 months in order to book profit