1.The current price of Facebook stock(Ticker:FB) IS 75.10/Share.Suppose the risk

Question

1.The current price of Facebook stock(Ticker:FB) IS 75.10/Share.Suppose the risk free rate is currently 2.4% at all maturities.FB does not pay a dividend and there is no expectation that it will anytime over the coming year.Consider a 7-month forward contract on FB(maturing in June).What is the forward price that would preclude arbitrage on such a forward contract?

(b)If the 7 month forward price on FB was $77.50, is there an arbitrage opportunity?If so, how would you exploit it?

(c)Suppose you had a long position in a forward contract on FB with F = $77.50/share(expiring in June), and by the time you get to May(one month remaining on the contract), FB's price has risen to $79.93. What is the value of your long contract?What would be the value of an analogous contract?

2.Now consider call and put options on FB expiring in June with strikes of K = 77.00(Kput = Kcall = 77.00). What is the largest lower bound on price of a call option on FB with K = 77.00 and T = June? What about the comparable put option?

Explanation / Answer

a) The forward price would be :-

$75.10*1.014 = $76.1514

Risk free Rate =2.4% for 12 months

So rate factor for 7 months would be {1 + (2.4/12*7)]= 1.014

b) We calculated the forward price to be $76.1514. Whereas the actual price is $77.50.

Clearly there is an arbitrage opportunity. The forward rate of FB is trading rich and we should go short.

Therefore Buy forward @ $77.50 and sell @ $76.1514.

Arbitrage Profit would be (77.50-76.1514) = $1.3486 x contract size

c) If we are long on FB @ $77.50 and price turns out to be $79.93, then we are at a profit of (79.93-77.50)

= $4.43

Analogous value of contact would be a loss of $4.43

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