Pinning stocks at expiration

There’s an excellent site that delves into research papers to find answers for questions raised by readers (CXO Advisory Group). Recently the topic was: Stock Price Pinning at Options Expiration?

A reader asked: “Do you have any research on the phenomenon of ‘pinning’ during options expiration? The theory is that there is a Max Pain price where options sellers stand to lose the least [MDW: It’s called Max Pain because it’s supposed to cause much pain for the buyers], and that they manipulate prices towards these levels.” A search of the Social Science Research Network (SSRN) separately for “pinning” and “expiration” yields the following studies, in descending order of number of downloads:

“Stock Price Clustering on Option Expiration Dates” from August 2004: “This paper presents striking evidence that option trading changes the prices of underlying stocks. In particular, we show that on expiration dates the closing prices of stocks with listed options cluster at option strike prices. On each expiration date, the returns of optionable stocks are altered by an average of at least 16.5 basis points, which translates into aggregate market capitalization shifts on the order of $9 billion. We provide evidence that hedge re-balancing by option market-makers and stock price manipulation by firm proprietary traders contribute to the clustering.”

We cannot argue with the facts, but interpretation of those facts is another matter. Max Pain theory suggests that market makers can pin stocks to the strike. The authors of this paper suggest that is exactly what happens. Their ‘evidence’? A $100 stock moves nearer to the strike price by $0.165. That’s not pinning by any definition of which I am aware. I understand that academics do research and the discovery of that small price shift is ‘evidence’ for them. However, in the real world of trading, it’s not that significant when you consider:

  • The pinning bet must be made in advance
  • The trader must pick the correct stocks because an average of 16 basis points is not very large
  • The trader must choose the right strike price
  • The strike that is closest right now may not turn out to be the correct strike price

Thus, the evidence that ‘proves’ pinning exists does exactly the opposite. It proves that it does not happen.

Let’s consider a situation in which the strike prices are 5 points apart. No option can be further OTM than 2.50 points. Pinning would result in a stock moving at least 2.00, and probably 2.25 points towards one strike. The fact that the observed moves are one sixth of one percent is ‘evidence’ that this phenomenon is something that we, as traders, cannot use.

Look at it this way: Every expiration, there are people who publish a list of stocks that finished right at, or very near, the strike price as proof of pinning. Nonsense. When strikes are 10 points apart, there are only 501 possibilities. Stocks can finish 5.00 points from the strike, or 4.99…..or 0.01 or right on the strike. Statistically that means that 11 out of every 500 stocks (Addendum: CORRECTED to: 2.2%) should finish within $0.05 of the strike. That is not pinning. That is randomness at work.

“The Effects of Option Expiration on NSE Volume and Prices” from November 2004: “This paper studies the effect of stock options expiration day on the underlying shares traded on the National Stock Exchange (NSE). Overall we tested for abnormal trading volume, abnormal price movement, individual stock reversal and stock pinning on expiration days. To the best of our knowledge, this is a first such study done on the Indian market.” Within the paper there is the following statement: “Stock pinning behavior on expiration days also was not suggested by the data for the five stocks considered…”

Five stocks is not much of a study, but one must begin somewhere. This paper says pinning is not observed.

“A Market-Induced Mechanism for Stock Pinning” from November 2003: “We propose a model to describe stock pinning on option expiration dates. We argue that if the open interest in a particular contract is unusually large, Delta-hedging in aggregate by floor market-makers can impact the stock price and drive it to the strike price of the option. We derive a stochastic differential equation for the stock price which has a singular drift that accounts for the price-impact of Delta-hedging. According to this model, the stock price has a finite probability of pinning at a strike. We calculate analytically and numerically this probability in terms of the volatility of the stock, the time-to-maturity, the open interest for the option under consideration and a “price-elasticity” constant that models price impact.”

No data is cited in this abstract, but that is quite a mouthful. Their argument has merit. When long calls, market makers (who are long ATM options) get longer as the stock rallies towards a strike. Thus they have stock to sell (to get neutral). This action reduces the chance that the stock will move away from the strike – to the upside.

On declines, MMs who are long puts get shorter as the stock moves through a strike. Thus, they have stock to buy (again to get neutral), reducing the chances of a further decline.

These effects may not be large, but that depends on just how many options (and how much positive gamma) these market makers own.

When market makers are short the options, and the stock moves towards the strike, it’s true that they would like to keep the stock near the strike price, but how can they do that? When short calls, as the stock moves toward and then through a strike, the MMs are short and getting shorter. Does anyone truly believe that these traders would go sell more stock short in an effort to pin the stock? A trader could go broke in a single day if he/she manifested that mentality. This argument is completely without merit. Those who are short would be more interested in buying stock in this scenario – further driving the price higher. They must protect themselves first, not risk going broke in an attempt to pin the stock.

Traders who are short puts would have the same problem on the downside as the stock approaches and moves through a strike. they would be more inclined to sell stock, rather than buy.

The first paper is probably the most relevant, but the stock price distortions it describes appear to be too small for exploitation, at least by individual traders. Moreover, the ascendancy of high-frequency trading (acceleration of dynamic hedging) since the sample periods used in these studies may have affected the speeds with which prices react to any apparent imbalances between options and their underlying assets.

I agree with that conclusion. Non-exploitable, even if it does occur.



6 Responses to Pinning stocks at expiration

  1. Tyler Craig 02/25/2011 at 9:03 AM #

    Great stuff Mark. Definitely one of the better explanations I’ve heard on pinning.

    • Mark D Wolfinger 02/25/2011 at 9:27 AM #

      This is a controversy that will never go away.


  2. Robert D. 02/25/2011 at 10:59 PM #


    Thanks for your thoughtful analysis on a controversial issue. For the sake of accuracy, though, 11 out of 500 is 2.2%, not 0.22%.


    • Mark D Wolfinger 02/26/2011 at 7:41 AM #

      Thank you Robert.


  3. Ed Hwong 02/28/2011 at 10:39 PM #

    Mark, on the same SSRN site, is a more specific paper regarding GOOG. Another options trader/author, Guy Cohen, coincidentally also mentioned GOOG in one of his books with regard to price manipulations. Are your thoughts the same with regard to this stock?


    • Mark D Wolfinger 02/28/2011 at 11:10 PM #


      I have no clue which stocks are manipulated and which are not.
      Wall Street is not an honest place.