# Gamma

#### DEFINITION of Gamma

Gamma is a derivative of the delta. This is the relationship between a derivative’s price and the price of its underlying asset.

#### WHAT IT IS IN ESSENCE

If some option has a large gamma, then its price movement in relation to the price movement of its underlying asset is volatile.

That increases both risk and reward. Because any price move in the underlying asset will be amplified in the price movement of its option. This derivative is always at its largest when a trade is at the money. Hence, the smallest when it is deeply in the money or out of the money.

In short, it is the movement of a delta in regard to the price of the underlying asset. As delta, this derivative is also one of the Greeks.

In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of derivatives. Like as options to a change in underlying parameters. The value of an instrument or portfolio of financial instruments is dependent on them.

The name is used because the most common of these sensitivities are denoted by Greek letters. As are some other financial measures.

Collectively these have also been called the risk sensitivities, risk measures, or hedge parameters.

HOW TO USE

Gamma trading is not simply the same thing as hedging.

Say you have a portfolio of options that have been delta hedged. Then this will often only be a delta-neutral portfolio versus a single price in the underlying product.

For example, imagine you own some calls and you are short some puts. To delta-hedge this options portfolio, you will need to sell some of the underlying. However, if the price of the underlying changes, then the delta-hedge you have executed is probably going to be inaccurate.

This is because the individual options in your portfolio have gamma. This means that their deltas change if the underlying product price changes.

So to remain delta-neutral, you will have to adjust your delta hedge. This adjustment to your overall delta is known as a gamma hedge.

#### Gamma trading really refers to the idea of looking to gamma hedge profitably.

For example, a trader may want to buy some options so that he is long gamma. This because he is thinking he can make a profit by this trading the underlying. What he means is that he thinks the price of owning the options day-to-day is less than the amount he can make from gamma hedging.