Using Options Gamma

Characteristics of Gamma

The gamma value of an option indicates how much the delta value of that option will increase for every $1 price increase in the underlying security or for every $1 price decrease in the underlying security. It's a positive number regardless of whether you are buying calls or puts – although it's effectively negative when you write options.

For example, imagine you have a call with a delta of .60. If the price of the underlying security rises by $1, then the price of the call would therefore rise by $.60. If the gamma value was .10, then the delta would increase to .70. This means that another $1 rise in the price of the underlying security would result in the price of the option increasing by $.70, and the delta would also increase again in accordance with the gamma.

This highlights how moneyness affects the delta value of an options contract, because when the contract gets deeper into the money, each price movement of the underlying security has a bigger effect on the price. The gamma is also affected by moneyness, and it decreases as an in the money contract moves further into the money.

This means that as a contract gets deeper into the money, the delta continues to increase but at a slower rate. The gamma of an out of the money contract would also decrease as it moved further out of the money. Therefore, gamma is typically at its highest for options that are at the money, or very near the money.

New let’s look at an example of an out of the money call, with a delta of .40 and a gamma of .10. If the price of the underlying security fell by $1, then the price of the call would fall by $.40 and the delta would fall to .30. The gamma would also fall, so if the underlying security fell by a further $1, the price of the call would fall by $.30, but the delta would fall by less than 1.

This again shows us how delta is affected by moneyness. This time highlighting how each price movement of the underlying security has less effect as an option gets further and further out of the money. However, when the gamma is also decreasing as the options move further out of the money, the rate at which the delta reduces slows down.

The above examples relate to calls, and it's important to compare how puts are affected by the combination of gamma and delta too. Essentially, the effect is the same and the gamma of a put also decreases as the put moves further into in the money or further out of the money, just like a call.

The biggest difference is simply that, because puts increase in price when the underlying security falls and decrease in price when the underlying security rises, puts have negative delta values. This means that the delta of a put moves towards 0 when the underlying security increases in price, and towards -1 when the underlying security falls in price. The delta of a call moves towards 1 when the underlying security increases in price and towards 0 when the underlying security falls in price.

The net effect of gamma is exactly the same though; it measures how a delta value has a larger effect on the price of an option because, that option becomes more and more in the money.

The gamma value is affected by the time left until expiration as well as moneyness. The gamma of options that are at the money will increase significantly as the expiration dates get closer, while the gamma of options that are either in the money or out of the money will move less significantly.

Putting Gamma to Use

In the first instance, if you are using very basic trades and simply buying either calls or puts to speculate on the price of an underlying security moving; gamma isn't hugely important yet. The positive gamma value of those options will, theoretically, ensure that the delta value of them will increase the further they get into the money: increasing the rate at which your profits grow, assuming the underlying security is moving in the right direction. The actual rate at which the delta value increases isn't really something you need to be too concerned with.

However, when you start using spreads and employing more complex strategies, the relationship between the gamma and the delta value of your overall position becomes more important. If you are using multiple positions effectively combined into one to speculate on the price of an underlying security moving, then you need to be clear on exactly what profile that overall position has.

For example, if your overall position has a positive delta and a positive gamma, then you will make profits if the price of the underlying security goes up, and continue to make profits the more it goes up as long as the delta value will always be increasing.

However, if your overall position has a positive delta and a negative gamma, then things are slightly different. You will still make profits if the price of the underlying security goes up, but the negative gamma means that the delta value will be moving towards 0. There will come a point when the position effectively reverses, because the delta value will become negative and your position will start losing money if the price of the underlying security continues to rise.

There's absolutely nothing wrong with entering such a trade, but you need to have an idea of at what point maximum profits have been reached and be ready to close your position at that point.

In very simple terms, it helps to remember the following. Buying either calls or puts will add positive gamma value to your overall position, while writing either calls or puts will add negative gamma value to your overall position. A positive value will mean the delta value becomes higher as the stock rises and lower as the stock falls, while a negative value will mean the delta value becomes lower as the stock falls, and higher as the stock rises.

The gamma is also important if you are making hedging trades, because you ideally want the value to be as low as possible so that your position is less affected by price movements in the underlying security.

Finally, it's also worth being aware of the relationship between gamma and theta. Generally speaking, high gamma means high theta. A high gamma means that you can make potentially higher exponential profits if the underlying security moves significantly in the right direction.

However, because such options typically come with a high theta value, the extrinsic value will be likely to decay at a fast rate. Therefore, you would need the underlying security to move quickly or you could potentially make substantial losses. This is another reason why an understanding of all the options Greeks is so important; it can affect a lot of the trading decisions you have to make.