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Pin Risk

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Pin risk is the tendency for a stock price the day of an option expiration to close at the strike price (if it is near it to begin with) of an option with a high open interest (outstanding contracts). For example, if a stock is trading around \$49 the day of expiration and the 50 strike calls or puts or both have a relatively high open interest (relative to the float and/or the average daily trading volume of the stock), the stock price will tend to gravitate toward \$50 by the end of the day. The reason for this is directly related to and helps explain gamma, the change in the delta of an option relative to the change in the stock price.

Let's say stock X is trading at \$49 on the day of expiration and that the 50 strike calls have an open interest of 10,000 options (equivalent to one million shares). The stock normally trades one million shares a day, so the open interest is fairly significant (a full day's trading volume). Sheryl has a delta neutral position of long 1000 (100,000 shares) 50 strike calls and short 38,000 shares (the current delta is .38). Remember, the delta can be viewed as the probability of the stock being in the money at expiration. By definition, the calls will either have a zero delta (if the stock price is below 50) or a one delta (if it is above 50) at the end of the day. As you can see, the gamma (change in delta) is extremely high.

One hour into trading the stock trades down to \$48. The probability of the stock price going above 50 dramatically falls (since there is not much time left) and the delta falls to only .25. Sheryl buys back 13,000 shares to be delta neutral. All of a sudden the stock rallies back up to \$49.25 and the delta quickly goes to .40. Sheryl sells back out 15,000 shares to be delta neutral. As you probably surmised, Sheryl is enjoying this high volatility, as every time she trades, she locks in a profit. She hopes it continues.

One hour goes by and not much happens to the stock price. Sheryl checks her deltas and is surprised to find that even though the stock price has not changed, the delta has dropped to .20. How did that happen? With only a few hours left now, the chance of the stock going above 50 has dropped to only 20%. This is why the gamma is so high for options that are expiring and are near the strike: time and price have an exponential affect on the delta.

Sheryl knows that if nothing happens she will just be short 40,000 shares of stock X by the end of the day since her options will expire out of the money. Even though she just sold the stock a few hours earlier at the same price, she now decides to buy it back to reduce her risk. Others with the same position start doing the same thing. This process begins to drive the stock up toward \$50. This continues for a while and soon the stock is right at \$50. The delta is now .50 and Sheryl sells shares again to get delta neutral. Notice that if the stock drops at all the high gamma will cause the delta to plunge again; every time it does so Sheryl becomes a buyer.

All of a sudden with an hour to go, the stock begins to rally as a buyer comes in (that seems to happen a lot lately). The stock pops to \$50.75 and the delta goes to .80. Sheryl realizes that if she does nothing in one hour she will now be net long 50,000 shares (1000 options less 50,000 shares short) and is currently delta long 30,000 shares. She quickly offers stock, but so do others. The buyer is filled with most of what he wants to buy and the stock begins to drift back down toward \$50.

As illustrated, because of the very high gamma of an expiring option, those with long option positions with a strike of 50 will become aggressive buyers of stock below 50 and aggressive sellers above 50 as they attempt to capture any deviation around that stock price and have no net long or short position in the stock after expiration. Normally after all is said and done, the long option trader will exercise just as many options as necessary to have a flat position after expiration. They will trade the stock as much as they can to squeeze out as much profit as possible (limited by transaction costs and just being tired). Volume is consequently often higher than average for stocks in this situation.

If the stock price is far enough away from the strike or if the open interest is very small, the normal buyers and sellers of the stock will have more influence over the short term stock price than the option traders. The distance from the strike and the consequential effect has to do with the volatility and liquidity of the stock. For example, a stock with a 30% volatility with a price within 1% or so of the strike price at expiration should experience pin risk. A stock with a 45% volatility may experience pin risk if it is even 2% away from the strike price.

Some may ask what about the traders with the short option positions: don't they offset the activity of the long option traders? The answer is sometimes, but usually not. They tend not to trade the stock and let the chips fall where they may. The exception would be if the stock begins to precipitously move away from the strike and they are uncomfortable with the amount of stock they will be left with. In these cases, they can exacerbate the movement of the stock, to the delight of the long option traders.
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No positions in stocks mentioned.

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