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By Lawrence G. McMillan

This article was originally published in The Option Strategist Newsletter Volume 11, No. 3 on February 14, 2002. 

In looking at some of the questions that have been submitted to us through the Q&A section of our web site and at the Intensive Option Seminar that was recently held in Boca Raton, FL, it is apparent that a number of them have to do with expiration – how an individual trader should handle a trade, what price index options are settled at, how arbitrage might affect the market or an individual stock, and so forth. This article will address all of the questions that have been asked, by interspersing the questions with commentary that answers the questions and expands on the concepts.

Is it true that a stock will tend to “hug” a strike price at expiration?

It is indeed true that options can drive a stock to “hug” a striking price at expiration. However, there is a logical explanation for this – arbitrage – not some conspiracy theory that the option market or market makers want to make sure that the most people lose their money. The way it works is this: suppose that a stock is trading at 47 with just a day remaining until February expiration, and there is substantial open interest in both the Feb 45 calls and the Feb 45 puts. By that late date, the Feb 45 call option will be trading at parity In fact, the scenario that is going to be described here can take place whenever an option that is just slightly in the money loses all of its time value premium. Usually that wouldn’t occur until there was just a day or two left in its life.

In this example, suppose that the markets for the Feb 45 call and the underlying stock, XYZ, are:

              Bid    Offer
XYZ Stock:    47.00  47.05
Feb 45 call:  1.95   2.10

Thus the call is bid at slightly less than parity. Actually the same scenario holds if the call is bid at parity, but we’ll use the discount assumption here to prove our point. Public customers who own the Feb 45 calls want to sell their options as expiration nears. Therefore, they sell at the bid. The buyer of that option is a market maker or an arbitrageur. When he buys the option, he doesn’t want to rely on the fact that XYZ stock will rise in price. Rather, he needs to hedge himself, so he sells XYZ common stock to hedge the call he just bought. At expiration, he will then exercise the call. So, from the arb’s viewpoint, his transactions are:

  Customer: sells 1 Feb 45 call @ 1.95
      Buys 1 Feb 45 call @ 1.95 debit
      Sells 100 XYZ at 47.00 credit (the bid)
  Exercise the Feb 45 calls, to
      Buy 100 XYZ at 45.00 debit
      Arb Profit: 0.05credit (profit).

The point here is not to show you how to execute profitable expiration arbitrage, but to show you what the arbs are doing. They are selling stock in the open market in this scenario. As more and more public customers come into the market to sell their expiring Feb 45 calls, the arbs’ activity involves selling more and more stock – each time they buy a call from a customer. This selling – in the absence of any other news-related influence on the stock – will result in the stock declining towards the strike price. Once the stock gets to the striking price, the call option will lose nearly all of its value and the public customers will no longer be selling the call.

Sometimes when this scenario occurs, you may even see the stock declining through the strike and trade below. It is then that put arbitrage cause the stock to rise. Without going into as much detail, the public customer who owns the expiring put sells it to the market maker. In this case, the market maker buys stock to hedge the put he just bought from the public customer. Enough of this buying will cause the stock to rise until it gets back to the striking price, in which case the activity will slack off.

So, on expiration day, the stock may be caught between the call arbitrage and the put arbitrage and therefore “hug” the strike. That’s what really happens.

Of course, that’s pretty boring stuff. No conspiracy theory there. However, that doesn’t prevent the X-filers from coming up with conspiracy theories. Usually, they’ll even say that a stock will tend to trade to the strike with the most open interest – beginning weeks before expiration. That is not true. It might, it might not. But there’s no logical explanation for why that should be true. I realize that my saying so won’t deter the conspiracy theorists, but I have designed a study to actually analyze the concept. Unfortunately I haven’t had time to implement the study, but I will get around to it one of these days.

How Do I Know What My Index Option is Worth At Expiration?

Index options have been around for nearly 20 years, and yet many customers and even some brokers don’t know about or understand the expiration settlement process – especially for the “a.m.” (morning) settlement options. Recently, we received a letter from a customer whose brokerage firm told him that his just-expired Dow Jones Index ($DJX) options would be worth the last trade price of the option! Obviously, that was a misinformed broker and not policy of the brokerage firm itself, but it does serve to show that there is misinformation about cash index option settlement.

The $DJX options, and most other cash-based sector and index options, expire with a morning settlement on the day of expiration – the third Friday of the expiration month.. This is called "a.m. settlement." $OEX options and a very few others settle at the close of trading on the 3rd Friday (“p.m. settlement”).

A holder of such an option will receive a value for them based on the settlement value of the index. The settlement value of an index that settles in the morning is computed by taking the first trade of each stock in the index on that day, and computing the value of the index using those prices for each individual stock. Thus the actual settlement price of the index may be a price that the index never traded at, due to the staggered openings of the individual stocks in the index.

The exchange itself posts the settlement value of the index. The settlement value isn't available, of course, until all of the individual stocks have opened on that Friday morning.

Afternoon (“p.m.”) settlement option use the closing price of each stock in the index, which results in the settlement price for these options being merely the closing price of the index itself. So those are easy to figure, but the “a.m.” settlements are impossible to calculate without a sophisticated computer. Thus, one must wait until the exchange itself releases the settlement value – usually sometime during that 3rd Friday, although sometimes not until after the market has closed. In the case of the Dow Jones and other indices whose options trade on the CBOE, the settlement value is posted on the CBOE's web site, under their "market statistics" page at: http://www.cboe.com/MktData/Settlement.asp

There is also a quote symbol associated with each settlement, but a lot of the quote vendors don't carry them. For $DJX, the symbol for the settlement value is $DJS.

If you go to the above link, you’ll see many of the other settlement symbols. For information from other exchanges, you’ll have to contact the exchange or have your broker do so.

Last month (January), the settlement price of the $DJX was 97.71, and it was used for all expiring January options. For example, a Jan 100 put settled at 2.29.

If you owned that put and did not sell it, you should receive a trade in your account on the next business day, showing that you sold all of your puts at a price of 2.29 (you will probably be charged a commission, although some firms reduce that commission since there wasn't any trade entered on the trading floor).

You should be sure to check your account at that time to make sure your options were settled at the correct price. There could be mistakes.

Of course, discovering the settlement value of a particular index in which you have held an option until expiration is mostly an academic exercise. There isn’t any trading that you can do to hedge your risk at that point; it is merely a matter of finding out at which price your option was closed out. If you are a seller of naked options, you should be careful because there have been a couple of times in the past where the index made a huge move for the “a.m.” settlement on Friday morning, but the actual value of the index was substantially different as the market moved quickly in the opposite direction. The most recent occurrence of this scenario was September, 2001, when stocks opened down heavily (thereby driving the “a.m.” settlement price well below the previous day’s low) but the market actually started to rally shortly after the opening and just kept on going up.

This article was originally published in The Option Strategist Newsletter Volume 11, No. 3 on February 14, 2002.  

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