6 Options II

S0 k 2 portfolio a one european call option

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Unformatted text preview: l time T, he ends up with stock worth ST, and he has sacrificed the interest he could have earned on K during the period from τ to T. • If he waits to exercise at T, he still has stock worth ST, but no sacrificed interest. • Another advantage of waiting is that if ST < K, then he does not want to exercise at all. If he had exercised early (paying K per share), he would regret the decision. Ec 174 OPTIONS II p. 4 of 18 3) If the stock price at time τ < T is Sτ > K, but might fall again before time T, an option holder might exercise early, buying at K and selling immediately at Sτ to get the payoff Sτ − K before it is too late. • If he exercises early and invests proceeds, he ends up with (Sτ – K)er(T−τ) at time T. • He can do better by short- selling the stock for Sτ today and investing it, then buying the stock back for K at time T to close his short position. He ends up with Sτer(T−τ) - K at time T, which is a bigger gain. 4) Conclusion - - if D = 0, then C = c. c) American- style call options (dividend- paying stocks). 1) If the stock pays dividends, it may be optimal to exercise an American call early, because a dividend will reduce the stock price Sτ. So C ≥ c. 2) Payoff = Sτ – K, so you want to exercise just before ex dividend date to get a higher St. d) American- style put options (stocks with or without dividends). 1) It may often be optimal to exercise American put options early, so P ≥ p. 2) An American put gives you the right to sell stock for K at any 0 < t < T. The payoff at time τ is K – Sτ. 3) If you hold a put and the stock price drops to some Sτ < K and you think it will drop no further, then the sooner you exercise the option the better, because you can invest the payoff K – Sτ at rate rf and end up with (K – Sτ)er(T−τ). Ec 174 OPTIONS II...
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