Understanding Option "Gamma"

When one is working towards understanding option gamma, it is first necessary to understand an option’s delta. In options trading there are a set of statistics that measure the sensitivity of the option to certain underlying factors - each is represented by a Greek letter, and they are collectively referred to as the Greeks. Gamma is a second derivative Greek that measures the rate of change of delta, which is the measurement of an option’s sensitivity to a change in the price of the underlying security. Reaching levels of significant complexity is attainable when considering the Greeks, but is not always necessary to successfully trade the instruments.

A Quick Look at Delta

An option’s delta is a measurement of how much the value of the option changes relative to a corresponding change in the value of the underlying security. Essentially, delta measures the amount by which an option’s price moves for a $1 change in the price of the underlying stock. Adding complexity to the concept, however, is the fact that delta is not constant at all price levels. Recall that an option’s price is made up of time value and intrinsic value. The value of an option tends to be increasingly sensitive to changes in the price of the underlying security as the option moves from far out-of-the-money, through at-the-money, and experiences a near dollar-for-dollar price change for options that are far in-the-money. This is explained by the fact that far in-the-money options are likely to receive near-parity returns in terms of intrinsic value - for every $1 increase in the price of the stock, there is a $1 increase in intrinsic value and, therefore, in the price of the option. Delta, then, is a non-constant factor that fluctuates as the price of the underlying stock changes.

The Value of Gamma


Given the fact that delta not only changes with the price of the underlying chart, but changes at a non-linear rate, a trader who is building an options trade that is meant to hedge his or her exposure to a certain stock, for example, wants to know how his position will change as the price of the stock changes. What is even more useful, when building a comprehensive hedge, is to understand at what rate the level of protection will change as the price of the underlying stock changes. Following the same example, a trader may find it useful to know that buying a certain option at current levels will give him $0.60 of protection for every $1 that the stock moves against him, but after the stock has moved by $2, his level of protection will have risen to $0.98 for every $1 move. The ability to judge these relationships gives the trader the ability to consider various option choices and to accurately gage both the cost and the quality of the hedges that are available. Using gamma can result in highly complex mathematical models to build effective hedges, but a basic understanding of the concept can help a less seasoned trader to understand some of the factors that affect movements in a given stock, the options written on that stock, and moves in the general market.

 

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