Pinning a Stock to a Strike Price at Expiration II

Part I.

When a
stock ends trading on expiration Friday, occasionally it finishes right
at the strike price, as probability theory says it must.  Those who
sold options at that strike price reap the maximum possible profit,
while those who own these options are unhappy.  The question is:  If
the stock is pinned in this situation, is it a natural event, or the
result of manipulation?

consider an option with a strike price of 90 and assume that this
strike price is nearest to being ATM (at the money).  When the
underlying stock ends trading for the day, the final price can be
anywhere between 87.51 and 92.50 (if it's not, then a different option
is nearest to the stock price).

are 500 different stock prices available.  If market makers (or anyone
else) were able to pin stocks to the strike, we ought to find a cluster
of closing prices at 90.00, or within a few pennies of 90.00.  If
pinning were a figment of people's imagination, then there would be no such
cluster, and final closing prices would be randomly distributed among
all 500 possible choices.

What Does The Evidence Show?

have been made and data has been collected.  I haven't made any effort
to compile a complete study, but if you Google an appropriate phrase,
I'm sure you can find more studies.

that those who own ATM options don't want to pin the stock, and those
who are short the options do.  Here are two studies that suggest a
small, but statistically significant cluster of closing prices that
surround the strike price.  In my opinion, the effect is too small to
concern the average individual investor.  If you are trading a multi-billion
dollar portfolio, then the possibility that pinning does occur to a small degree may become significant.


One academic study (2004)

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."

I am not in position to argue with the academics who published this study.  But these results do nothing to convince me that a stock can be pinned – when pinning really means making the closing price equal the strike price.


certain circumstances,pinning can be caused by floor traders faced with
delta-hedging long-gamma position on a single strike with an unusually
high open interest. In such cases, the demand and supply of deltas
around the strike can have a significant price impact and may drive the
price of the stock to the strike price."

study shows how those who own the options may unintentionally move the
stock nearer to the strike by normal hedging activities.  When the
stock moves above the strike price, the call delta moves towards 100
and the trader becomes longer.  Thus, shares are sold to make the
position more neutral.  Those sales can help drive the stock price
lower.  Similarly, when the stock drops below the strike price, the
call delta moves towards zero and the trader becomes short.  Shares
are purchased (driving the stock higher, towards the strike) to
neutralize the position.

Similarly, put owners play the same game.  When the stock rallies through the strike, the put delta shrinks and the trader gets longer and thus, sells shares.  When the stock drops below the strike, the trader becomes shorter and buys shares.

traders own those options, it's in their best interest to have the
stock finish away from the strike price.  Yet, this study suggests that
– against their own wishes – traders may help drive the stock closer to
the strike price.


I was on the CBOE trading floor (>20 years), I never heard of anyone
making a serious attempt to pin a stock to a strike price.  I found
zero evidence that 'those on the floor will hunt down strike prices
like heat-seeking missiles' and pin those stocks to the strike.  And with today's risk-avoidance mentality, I cannot conceive of the possibility that anyone would attempt to pin a stock.

true that the studies cited found a small effect in the stock's closing
price on expiration Friday, but only when that price was already near
the strike price.  If anyone wants to conclude that this provides
evidence that stocks can be pinned to the strike price, so be it.  But
to me, this is evidence to the contrary.


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