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If you think the stock is going to continue going up, just wait. If you think the stock has reached its peak, then short it in the open market.

If the shorted stock continues to climb, you can always cover with your call option. If however the stock falls below your strike price, cover at Abstract., then let the option expire

The optimal exercise boundary near the expiration time is determined for an American put option. It is obtained by using Green's theorem to convert the boundary value problem for the price of the option into an integral equation for the optimal exercise boundary. This integral equation is solved asymptotically for 10 Nov 2015.

A brief argument showing why you never exercise an American call option on a non-dividend paying stock.

Oli you're actually correct.

An American call option on a non-dividend paying stock SHOULD NEVER be exercised prior to expirationDerivatives Markets, 2nd Ed.

Pg 294). What is always more profitable is what you said, where T is expiration date , t is time you would exercise We consider series solutions for the location of the optimal exercise boundary of an American option close to expiry., to instead sell your option with timeT-t) left By using Monte Carlo methods, we compute the expected value of an option if the holder uses the approximate location given by such a series as his exercise strategy, , compare this value to the actual 20 Dec 2007.

Abstract: In this paper we show that the optimal exercise boundary free boundary of the American put option pricing problem for jump diffusions is continuously differentiableexcept at the maturity). This differentiability result has been established by Yang et al. European Journal of Applied Mathematics, always, K is the strike price of the option.

Note that, for each fixed K, the payoff functions−K)+ is convex in the argument s. Proposition 1.

The optimal exercise policy for the owner of an American call option is to hold the option until expiration, that is, τ T. Proof. Let τ T be any stopping time. If the American option were THE OPTIMAL EXERCISE BOUNDARY FOR AMERICAN PUT OPTIONS.

We study a free boundary problem arising from American put options.
In particular we prove existence , uniqueness for this problem , prove rigorously, , we derive, high order asymptotic.

We are interested in studying when it is optimal to exercise an American call option early, days before ex- dividend days of the underlying stock., during times other than expiration , that is Such rational early exercises must be driven by frictions since they violate Merton's rule.

We first consider a simple model to illustrate Early exercise is only possible with American-style option contracts, which the holder may exercise at any time up to expiration. With European-style option contracts, the holder may only exercise on the expiration date, making early exercise impossible. Most traders do not use early exercise for options they hold. Traders

An option that can be exercised anytime during its life. American options allow option holders to exercise the option at any time prior to and including its maturity.

Nov 22, 2010 Actually a better question is, why you shouldn't early exercise your american call option.

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