\begin{tabular}{|l|l|l|l|l|l|} \hline Option & Strike & Expiration & Option price & Implied Vol & Delta(Option/S) \\ \hline PUT & $30 & 6 -months & $0.14 & 40% & -0.023 \\ \hline PUT & $40 & 6 months & $0.77 & 32% & -0.123 \\ \hline PUT & $50 & 6 -months & $2.74 & 22% & -0.431 \\ \hline PUT & $50.75 & 6 -months & $2.97 & 21% & -0.470 \\ \hline & & & & & \\ \hline CALL & $50 & 6 -months & $3.48 & 22% & 0.569 \\ \hline CALL & $50.75 & 6 -months & $2.97 & 21% & 0.530 \\ \hline CALL & $55 & 6 -months & $1.20 & 19% & 0.299 \\ \hline CALL & $60 & 6 -months & $0.15 & 15% & 0.065 \\ \hline \end{tabular} a) Recall the general formula (in terms of S(t),r,q,t,T) for the forward price of a stock for delivery date T : [ Forward price for delivery date T]=S(t)exp((rq)(Tt)) In this example, is the forward price for delivery in 6 months higher or lower than the current price of $50 ? b) The put-call parity relationship: [Price of K STRIKE CALL (Expiry T)] - [Price of K Strike PUT (Expiry T)]= [Value of Forward contact with invoice price K (Delivery date T) ] Looking at the table. At what strike do the put and the call have the same value? Is this consistent with put-call parity? c) Put-call parity relationship: CK(S,t)PK(S,t)=VK(S,t) Where the subscript " K " means strike =K (for the two option C and P ) and invoice price =K (for the forward contract V) Assume that the dividend rate is zero (like we have here). Take the derivative with respect to the current stock price S of the put-call parity relationship. Show that: (DELTA of CALL)(DELTA of PUT )=1 Do we see this relationship appearing in the table above