AIG stock sells at $61.21 and the 6-month 60-strike put is selling at $3.20. The

Question

AIG stock sells at $61.21 and the 6-month 60-strike put is selling at $3.20. The risk-free rate is 4% and the stock will pay a dividend of $0.30 in 3 months. We assume that all options are European-style.

(a) What is the theoretical price of the 6-month 60-strike call?

(b) The 6-month call is selling at $4.95 on the market, show how you can benefit from this arbitrage opportunity. Show all details.

(c) If the options above were American-style, will there still be an arbitrage opportunity?

Please be specific and show all the arbitrage for part b

Explanation / Answer

a) F (T)= S0(1 + Rf )^t E[Dt ]

Where Ft is thoeritical price = have to find

S0- selling price of stock (INdex price) = 61.21

Rf = risk free rate = 4%

Dt= dividend

t= 6 months = .5 years

61.21*(1+.04)^.5 - 0.30 = $62.12 ----------------- answer

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