| From MrSwing.com When Does Early Exercise Make Sense, and Dollars? Stan Freifeld - May 9, 2008
In order for it to make sense to early exercise an option, there must be some positive cash flow that results from the exercise. We'll look at Calls and Puts separately to determine when the early exercise is the right way to go. First we'll need to remember 2 of our 6 basic synthetic equations; namely,
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:
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.
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:
Recognizing that the Long Stock and Short Call is synthetically a Short Put, we get:
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.
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. © Copyright 2008 by MrSwing.com |