This week I want to talk about the early exercise of options. When you buy an option, you get a right. Obviously I'm talking about American style options, since European options can only be exercised at expiration. Let's examine when does it make sense to take advantage of this right to exercise the option?

When a long option position is put on, there are several things that can be done to close the position:

1) You can sell the option,
2) You can exercise the option, or
3) You can hold the option to expiration, at which time it will either be worthless or equal to parity, i.e., Stock - Strike for a Call, and Strike - Stock for a Put.

I'm sure that you remember that an options' value is made up of both intrinsic value and time value. When an option is exercised any remaining time value is lost. So our first criteria as to when to early exercise is for the option to be deep in the money and have a delta very close to 100. A 98 or 99 delta option may also be a candidate, but the closer to 100 the better.

Long Call = Long Stock + Long Put
Long Put = Short Stock + Long Call

Let's assume that we had no position on. Well, no position is the same as having a Long Call, and also having the exact same Short Call on at the same time. So to put this into the form of an equation, we can say:

Long Call + Short Call = 0

Now remember, we want to know when we would get a positive cash flow by exercising the Long Call, i.e., under what circumstances will exercising the Call give us a value greater than 0.

Or, when is: exercised Long Call + Short Call > 0

What happens when the Long Call is exercised? We lose the Call and we get Long Stock and any Dividends (D), but we have to finance the stock by paying interest on the Strike price from now through expiration. We'll call this "I".

So substituting for the exercised Long Call we get:

Long Stock + D - I + Short Call > 0

Recognizing that the Long Stock and Short Call is synthetically a Short Put, we get:

Short Put + D - I > 0 and then transposing the Short Put to the other side of the inequality (where it then becomes a Long Put) we finally get the result, phew!

D - I > Long Put

So what does it mean? First, in the case of a stock that does not pay dividends, i.e., D = 0, it never pays to exercise a Call early. If the stock does pay a dividend, we would want to wait as long as possible before exercising (to minimize I), but still capture the dividend. When does this happen? You got it - on the day before the stock goes ex-dividend. Don't worry if you didn't completely follow how we got there, however, the results are very important and are boldly restated:

On a non-dividend paying stock, it NEVER pays to early exercise a Call option.

On a dividend paying stock, the only time it MAY pay to exercise a Call option is the day before the stock goes ex-dividend, and only if the dividend minus the cost of carry is less than the corresponding Put.

Basically, you can think of it as exercising the Call, under the right conditions, to get the dividend.

Okay, what about Puts, when do we exercise them? The demonstration is very similar, so I'll go through it without all the explanation. If you have trouble following the steps, send me an email.

Long Put + Short Put = 0
exercised Long Put + Short Put > 0
Short Stock -D + I + Short Put > 0
Short Call - D + I > 0
I - D > Long Call

The results here are a little different, and you have to be a little more careful. If the stock is non-dividend paying then the only time you would exercise the Put is when the cost of carry is greater than the corresponding Call. When would this be likely to occur? The Put would have to be deep in the money, and some combination of high interest rates and low volatility.

When the stock does pay a dividend then the time to check would generally be after the dividend is paid, i.e., after the ex-dividend date when it's now equal to 0, although if the dividend is small enough, there are situations where it might make sense to exercise the Put even before the ex-date.

Now if you think all these calculations are too complicated, don't worry. There are platforms and software available, although I'm not sure which ones, which will identify when you should do the early exercise.

A final point on early exercise. I've had students tell me that they don't want to short in the money options for fear of being assigned. Let's put that one to bed. If you're short a deep in the money option and you get assigned, you're basically in the same position. The option you were short had a delta close to 100 for Puts and -100 for Calls. So when you find out you've been assigned and that it creates a cash-flow issue, you call your broker and either sell the long stock and sell another less deep in the money Put, or buy back the short stock and sell a less deep in the money Call. Truth is, if you are short deep in the money options that meet the criteria for being exercised and they're not assigned, then that's actually a benefit for you. In fact, this concept is what "dividend plays" are all about, but that's for another article.