6 Options II

# S0 k 2 portfolio a one european call option

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 &lt; 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 &lt; T is Sτ &gt; 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 &lt; t &lt; T. The payoff at time τ is K – Sτ. 3) If you hold a put and the stock price drops to some Sτ &lt; 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...
View Full Document

Ask a homework question - tutors are online