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I have noticed a number of posts recently that have skirted around the subject of spreads with "negative gamma" (or "short gamma", if you prefer). I thought it might be worth discussing a little.

If you are doing much option trading and do not already know some basics about delta and gamma, you are probably skating on very thin ice. You may get away with it, for a while, but there is likely to be a very rude surprise in your future.

Under the assumption that there are some potential option traders reading this who do not have much background, I'll try to give a quick (meaning incomplete) review of them.

The delta of an option is the amount an option is expected to change in price if the underlying goes up one point (or go down if the underlying goes down a point). Since call options are expected to go up in value if the stock goes up, the delta of a call option is always positive. Similarly, put options are expected to go down in value if the stock goes up a point, so the delta of a put option is always negative.

There are two different conventions used to give the value of delta (or any of the other "greeks"). One is the amount the quoted price is expected to change. By this convention, the value of a call delta ranges from a low of 0.00 to a high of 1.00. The other is the amount the cost of a contract for 100 units is expected to change. By this convention the value of a call delta ranges from a low of 0 to a high of 100, and the value of a put delta ranges from a low of -100 to a high of 0. I will use the per contract values in this discussion.

If we look at options near expiration, it should be obvious that an option that is way out of the money will have a delta close to zero. The option is essentially worthless and the underlying moving one point is not going to change that. Similary, an option deep in the money will have a delta close to 100 for a call or -100 for a put. The deep in the money contract will have become a surrogate for a position in the underlying. A one point change in the value of the underlying will be expected to change the value of the option about $100. Near expiration, an at the money call option has a delta of about 50 and an at the money put option has a delta of about -50.

Since we know different options (based on a comparison of the strike price to the price of the underlying) have different deltas, it is clear the value of delta for a particular option changes as the value of the underlying change. The amount delta changes when the underlying moves up one point is called gamma. The value of gamma is always positive for all options; it does not matter if it is a call or a put.

Close to expiration, the gamma of a far out of the money option (or a deep in the money option) will be close to zero. The maximum value of gamma will be on the at the money options.

For an example of how this works, let's look at the August options with a strike of 55 on GE. (I tend to use GE in examples simply because it has the largest market cap, not because I think it is a good stock upon which to trade options.)

GE closed at 54 1/8.
The average of the bid and ask for the calls is 1.65625.
The average of the bid and ask for the puts is 2.1875.
The calls have a delta of 46.01 and a gamma of 8.84.
The puts have a delta of -54.61 and a gamma of 9.58.

If these were the quotes 5 minutes before the close, and I bought one of the calls for $165.625 and one of the puts for $218.75, and the stock had moved one or two points before closing, what would I expect the options to be worth?

If the close was 55 1/8 I would adjust by the delta, so the expected values would be:

For the call: $165.625 + $46.01 = $211.635
For the put: $218.75 + -$56.61 = $162.14

The deltas would now be:

For the call: 46.01 + 8.84 = 54.85
For the put: -54.61 + 9.58 = 45.03

So, if the close was at 56 1/8 I would expect the options to be:

For the call: $211.635 + 54.85 = $266.515
For the put: $162.14 + -$45.03 = $117.11

Similarly, if the stock had gone down 1 point and closed at 53 1/8, the expected values for the options would be:

For the call: $165.625 - $46.01 = $119.615
For the put: $218.75 - -$56.61 = $275.36

The deltas would now be:

For the call: 46.01 - 8.84 = 37.17
For the put: -54.61 - 9.58 = -64.19

So if the stock had gone down two points, to 52 1/8, the expected value of the options would be:

For the call: $119.615 - $37.17 = $82.445
For the put: $275.36 - -$64.19 = $339.55

I want to make one more quick point. The underlying, such as 100 shares of stock, always has a delta of 100 and a gamma of zero. This should be clear since, regardless on the stock price, a one point rise in the price will increase the value of the position by $100.

This is far from a complete discussion of delta and gamma. I have not mentioned significant apects of gamma, such as the way gamma changes value as the price of the underlying changes. I only wanted to give enough background to allow people less familiar with gamma to follow the rest of the discussion.

Instead of one giant post, I will add to this thread in additional posts to get into some of the considerations associated with gamma.
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