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?
3. Suppose instead of the forward contract on FB described in (1) , you own 10000 shares of FB. Moreover, you observe the following prices on options. Moreover, you observe the following prices on options on FB expiring in June(in approximately 7 months)
Strike(K) Calls Puts Strike(K) Calls Puts
73 7.93 4.55 78 5.55 7.20
74 7.43 5.05 80 4.65 8.75
75 6.93 5.55 82.50 3.85 10.45
76 6.45 6.05 85 3.20 12.30
77 6.00 6.60 87.50 2.64 14.23
a) Given that the price of FB is currently $75.10/share, which of the above options are in the money?
(b) Assume you are nervous about your holding in FB and you are considering buying a "protective put" on FB with K=$75/hr, but this is expensive so you decide to "cheapen". Provide at least three strategies that are less expensive than buying an at the money option. What are the costs of your three strategies?
(c) Draw a graph of the payoff of the two strategies below(make sure to label each graph with the strategy described above)
(d) Distinguish between a short straddle at K = 75 and a butterfly spread using calls and or/puts whose strikes are 73,75 and 77.