Wednesday, October 04, 2006

The Real Reason Stocks Often Times "Pin" A Strike Price When Options Expire

For a long time, I have heard (and read) a great deal of misinformation about the tendency of stock prices to “pin” a strike price on an options expiration day.

I will attempt to explain the mechanics involved that lead to stocks “pinning” a strike price (no conspiracy theories). For the sake of making this explanation relatively brief, I am working under the assumption that you have, at least, a basic understanding of stock options (delta, gamma, implied volatility, and put-call parity are the most advanced concepts that you need to understand in order to follow my explanation).

This explanation runs contrary to the “Max-Pain” explanation, in that “Max-Pain” says that the small traders are the ones who are buying options while the “big money” institutions are selling options (to the small trader) and because the “big money” wants to pay out as little money as possible when options expire, they use their “firepower” to make sure that happens.

Here it goes …

(Note: When I mention a dealer’s “net position,” “net delta,” or any other reference to the dealer’s portfolio, I am talking about a specific portion of that dealer’s portfolio – the portion that is devoted to hedging its options position in XYZ stock.)

A declining implied volatility on a stock’s options indicates that people are selling options. Due to put-call parity, it’s really not that important whether the options are calls or puts.

Options dealers (I am lumping market makers, specialists, trading desks … into this one “generic” category) TEND to be delta-neutral (at least they have a much greater tendency to be delta-neutral than the options-trading public as a whole).

If the options-trading public, as a whole, are net sellers of XYZ options, then the dealers will be net buyers of XYZ options.

The dealers will hedge their long (short) delta position (if the dealers are net-long puts, then they have a net-short delta position; if the dealers are net-long calls, then they have a net-long delta position) by selling (buying) XYZ stock. In practice, the dealers often times hedge their delta position by buying and/or selling other XYZ options, but at some point, those options are being hedged with XYZ stock.

At this point, the dealer's are hedged … partially.

The dealers are delta-neutral, but because delta is ever-changing (it is “dynamic”), a small move in the price of XYZ stock can cause that dealer’s portfolio to have a slightly positive or negative delta (a move in interest rates, dividends, time, and implied volatility can also affect an option’s delta, but for the sake of illustration, it’s easier to have only one variable).

Because the dealers are net long XYZ options, they are also long gamma.

Since the dealers are long gamma, they must buy stock as the stock moves lower and sell stock as it moves higher (meaning that they must "fade" the market to remain delta neutral).

Let me give a simplified example:

XYZ stock is @ 50.
The dealer is long 100 of the XYZ (front-month) 50 calls (delta of .50 & gamma of .14).
The dealer is long 100 of the XYZ (front-month) 50 puts (delta of -.50 & gamma of .14).

At this point the dealer’s net-delta is 0 ([100 calls x .50 delta] + [100 puts x -.50 delta] = 0).

If the stock moves up 1 point (to 51) and the dealer has not yet re-hedged his position, he will have a net-delta of 28 ([100 calls x .64 delta] + [100 puts x -.36 delta] = 28).

The dealer must now sell 2800 shares of XYZ stock to get back to delta-neutral.

So, as XYZ stock moved higher, the dealer sold shares.

In practice, things aren't so “jerky,” meaning that dealers typically make several small moves to re-hedge, not fewer large moves.

As expiration approaches, gamma increases (for at-the-money and near-the-money options), which means that the influence that options have on stocks also increases.

It’s also worth noting that, as an option’s implied volatility decreases, the gamma on those options increases (for at-the-money or near-the-money options), which acts as another influence causing options to gravitate towards a strike price.

Let me give another example (less simplified than the previous example).

XYZ stock is @ 50.
The implied volatility on the XYZ (front-month) 50 calls is 25% (and remains at 25%).

With 20 days to expiration, the gamma for those calls will be about .14.
With 5 days to expiration, the gamma is about .27.

If the implied volatility on the options was 50% (and remained at 50%) …

With 20 days to expiration, the gamma for those calls will be about .07.
With 5 days to expiration, the gamma is about .14.

It’s no too difficult to see why a stock that has a high amount of open interest (in at-the-money and near-the-money options) in relation to its volume on a given options expiration day will “pin,” or nearly “pin,” a strike price when options expire.

I don't want to discount the role that a “self-fulfilling prophecy” plays in strike-price-“pinning.” If a stock “feels” like it wants to pin a strike price, many traders won't fight it – they'll simply move on to another stock.


Daniel said...

Great summary. And thanks for putting the lie to the conspiracy theories.

Of course, it's always easier to blame faceless fatcats or greedy wall street traders than it is to think through the math and logic of why a phenomenon can happen.

Dan @ Casual Kitchen

Jack said...

I do agree. Indeed, great summary. The best thing is that you described all things very clearly. Of course, Dealers has to buy stock only when stock moves lower and sell stock as it moves higher. Cheers!
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