DERIVATIVES ' R US/V1N6/American vs. European Puts
VOLUME 1, NUMBER 6, March 27, 1995
Last week I covered the difference between American and European calls for options on assets (in contrast to options on futures). This week I'm covering the difference between American and European puts.
American puts on stocks without dividends always have some possibility of being exercised early. For example, suppose you owned an American put on a stock that went bankrupt. By bankrupt, I mean that it is dead and will not come back to life. Consequently the stock is worth zero. In that case, you are holding an option to sell the stock for the strike and there is absolutely nothing gained by waiting until expiration to exercise it.
The bankruptcy case is one obvious situation but bankruptcy is not required to justify early exercise. Let's look at a more likely case.
Suppose you are holding an American put at expiration. The strike is $100. Let the stock be worth less than $100. You exercise the put and pick up the difference between the stock price and $100. Had you exercised it early you would be better off because you would have gotten the $100 earlier and could have picked up the interest on it. You could have shorted the stock at that time and covered the short position at expiration. In other words, if you know the put will end up in the money, you might as well exercise it early.
Suppose the put ends up out of the money. Had you exercised it early you would have picked up the $100 early, invested it to earn some interest and you could have shorted the stock at whatever its price was at that time. Now at expiration you cover the short position. If the stock price now at expiration exceeds the exercise price plus the interest you earned on it, you'll end up with a deficiency and you'll wish you had not exercised it early. Thus, if the stock price ends up above the strike, it is possible that you would have been better off exercising early but it is possible that you would have been better off waiting. As noted above, if the stock ends up below the strike, you'll definitely be better off having exercised early. Of course, all of this is after the fact and proves only one thing - you could conceivably be better off exercising early.
Finding out exactly when to exercise early is a difficult task and can be accurately computed only with an American put option pricing model or procedure, like the binomial model. Some approximation methods, however, are available. It is easy to say that you exercise when the market price is driven to the exercise value but then you are just following the market, which had to have used an option pricing model to establish that the current market price is the exercise value.
Dividends complicate things quite a bit. When a company pays a dividend it helps put option holders because it works to constrain the stock's growth. Consequently, early exercise is less likely to occur the higher the dividends. When early exercise is justified, it will nearly always be the case that it should be done immediately after the stock goes ex-dividend. Again, an option pricing model is necessary to tell you when the optimal time to exercise early occurs. I plan to later cover the option pricing models and this issue will resurface.
BACK ISSUES: Back issues are available by anonymous ftp from fbox.vt.edu/filebox/business/finance/dmc/DRU or can be accessed using a Web browser at http:fbox.vt.edu:10021/business/finance/dmc/DRU