American Option Exercise: Dividends, Time Value, and Interest Rates

# Early exercise of American options


# Early exercise of American options












I know this question is considered basic and has been asked millions of times, but I have done my research and there are some points that I just can't understand.

- For an American call, many resources say that it's possible to early exercise right before a dividend if the dividend is worth more than the remaining time value. But if you exercise the call before the dividend and acquire the stock to capture the dividend, then right after the dividend payment, the stock price will drop by the exact amount of the dividend payment and your overall payoff will still be $S_t - K$ where $S_t$ is the stock price right before the dividend payment. So from my understanding it will still be better to sell the call option before the dividend payment as the payoff is $S_t - K$ plus the time value. Does it mean that this argument is invalid?

- Many say that if an American put is deep-in-the-money, it might be optimal to early exercise even in absence of dividend. What confuses me is that in any case where you decide to early exercise, your payoff will only be the intrinsic value, will it not always be better to sell the put option directly?

## Answer by Brian B (score 7, accepted)

https://quant.stackexchange.com/a/37609

It is easiest to just think about volatility dropping to near zero in each of these cases, and also to assume that you will immediately trade out of the stock position. Note the following principles apply when effective interest rate $r>0$.

Note that you already own the option(s) in question, so we can just compare the profit of the various exercise strategies.

- For the call, the profit of an early exercise is $S - K$. The expected profit of future exercise is $e^{rt}(S-D)-K$ which has present value $S - D - e^{-rt}K$. We can rewrite that as $S - K - (D - (1-e^{-rt})K)$, which shows where the (zero-vol) threshold of dividend size must be to make the proposition attractive.

- For the put, the exercise value now is $K-S$, and the expected profit of future exercise is $K-e^{rt}S$ which has present value $e^{-rt}K-S$. It is always better to exercise the put option when volatility is zero and $r>0$.

## Answer by Bob Baerker (score 1)

https://quant.stackexchange.com/a/58410

Your understanding is correct. It makes no sense to exercise a call (as well as a put) when there is time premium remaining because you are throwing away that time premium by doing so. Sell the call and buy the stock if you want to own it in order to capture the dividend.

Buying the stock to capture the dividend makes no sense to me if it's a non sheltered account because since share price is reduced by the exact amount of the dividend on the ex-div date, you're incurring a taxable event with zero total return from the process and therefore you are effectively going to pay taxes for the privilege of receiving some of your own money from your equity position.

OTOH, if the bid of an ITM option is less than its intrinsic value then it makes sense to exercise it in order to avoid the haircut. Take the opposing equity position first and then exercising, thereby avoiding leg out risk.