I have a problem getting my head around the following 'fact' regarding an American option: that it never makes sense to exercise the option before expiry if the underlying asset pays a dividend.My thoughts:1. I can understand this argument if an option that is at-the-money is exercised after a dividend payment, since this payment would likely send the option out of the money.2. I can also understand the argument that early exercise of the option destroys its time value.However, what happens if an option is deep in the money some time during the exercise period? Why would it not make sense to exercise it then?Thanks in advance.

I think you meant that it is never optimal to exercise an American option before expiration when the underlying asset does not pay a dividend. The reason for this is that, even if the option is deep in-the-money, then someone should be willing to pay for that option given that value (Stock Price - Strike Price) plus time value (and positive probability of getting deeper into the money). Hence, neglecting transactions costs, it will always demand a higher price rather than just exercising it as (Stock Price - Strike Price).

Well, it has a positive probability of going out-of-the-money too. So the question really is, why is the time value always positive for a call option whether it is in-the-money or out-of-the-money?The standard proof uses put-call parity, c - p = S - Xe^(-rT) > S - X => c > S - X. This already tells us that the answer has nothing to do with the nature of the underlying process because put-call parity is independent of that.What is the intuitive reason then?QuoteOriginally posted by: csaI think you meant that it is never optimal to exercise an American option before expiration when the underlying asset does not pay a dividend. The reason for this is that, even if the option is deep in-the-money, then someone should be willing to pay for that option given that value (Stock Price - Strike Price) plus time value (and positive probability of getting deeper into the money). Hence, neglecting transactions costs, it will always demand a higher price rather than just exercising it as (Stock Price - Strike Price).

Check on the "dividend capture" strategy. I know that in the early '80s American calls on dividend paying stocks were exercised just prior to the record date to capture the underlying dividend. I can't remember the exact reasoning, other than the desire for income.Mike How about this '86 FM paper:Link

QuoteOriginally posted by: anuj76However, what happens if an option is deep in the money some time during the exercise period? Why would it not make sense to exercise it then?Let assume you have a very deep in the money call (delta=1, time value=0)If you exercise the option you earn only the intrinsic value (S-K).However there is a better strategy: you can sell the underlying stock locking the intrinsic value and invest the proceeds at the risk free rate.Your payoff at expiry will be: [S(t)-K] -S(t) +S(0)*exp(rt)Discounting at the risk free rate the value of the portfolio is S(0)- K*exp(-rt) > intrinsic valueNote that this is the same result of Black & Scholes formula when N(d1)=N(d2)=1P.