Wednesday, October 04, 2006

Why Does Options Expiration Sometimes Add Volatility To A Stock?

This is the counterpart to a piece that I wrote about stocks “pinning” a strike price.

I will discuss the reason why the expiration of stock options can add volatility to a stock.

A increasing implied volatility on a stock’s options indicates that people are buying 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-buyers of XYZ options, then the dealers will be net-sellers of XYZ options.

The dealers will hedge their long (short) delta position (if the dealers are net-short puts, then they have a net-long delta position; if the dealers are net-short calls, then they have a net-short 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 (at adjacent strike prices and/or expirations), 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-short XYZ options, they are also short gamma.

Since the dealers are short gamma, they must buy stock as the stock moves higher and sell stock as it moves lower (meaning that, in order to remain delta neutral, they must exasperate volatility).

Let me give a simplified example:

XYZ stock is @ 50.
The dealer is short 100 of the XYZ (front-month) 50 calls (delta of .50 & gamma of .14).
The dealer is short 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 buy 2800 shares of XYZ stock to get back to delta-neutral.

So, as XYZ stock moved higher, the dealer bought 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.

Let me give another 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 a trader had a large short options position and the stock started to quickly move against him, that trader might panic and exit his short options position, which would make the dealers’ gamma position “shorter” than it was previously. That would mean that the dealers would have to buy (sell) even more stock on rallies (sell-offs).

For that reason, a sharp increase of implied volatility in the options of a stock that is accompanied by a large move in price of the underlying stock can cause a “hot knife through butter” type of move.

It is my belief that those types of moves are most likely to happen in the following situation:

A stock’s options previously had a low implied volatility (meaning that there were a lot of options sellers).

The stock managed to break the gravitational pull of a strike price (those traders who were short options are now beginning to loose money – rapidly).

The traders who were short the options, start to panic and exit their short options positions (i.e. they are buying when the MUST, not when they WANT), driving up implied volatilies of the options on that stock (and making dealers “shorter” gamma, which further exaserbates price moves in the stock).

The above scenario is one where the implied volatily of the options was relatively low, but it increased at a rapid rate. What makes the situation even worse (for the trader who is short options) is the fact that not all options traders are going to cover their short options position at the same time – some will have a higher threshold for pain than others. That can make the effects of added volatility (options-induced) even greater.

It’s also important to note that a stock that is having a “hot knife through butter” move is going to attract a lot of attention, thus making volatility even greater.

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