Sheridan Options Mentoring Blog |  |
| Lessons in Greek: Delta and Gamma Posted: 19 May 2011 08:55 AM PDT
The vocabulary of an options trader is quite different from that of the stock trader and often represents a major point of confusion to students first studying options. One of the areas that can be confusing is the understanding and the impact of the "Greeks" on positions. I thought it would be helpful to visit the Greeks in order to refresh our knowledge of them and touch a bit on their usefulness to the options trader. A thorough familiarity with these terms can help provide both a means of communicating concepts and analyzing trades. The most important "Greeks" are delta, theta, and vega. These variables represent the impact of price change, time passage, and changes in implied volatility for both individual options and multi-legged option positions. A fourth major Greek is gamma and represents the change in delta as price of the underlying changes. Math majors among readers will recognize that gamma is the second derivative of delta. While I admit that "vega" is not really a true Greek character it is in longstanding use in optionspeak. Delta is a measure of the correlation of price change of an option relative to the price change of the underlying. It is a very dynamic attribute and can potentially range from 0 to 1 for individual calls and 0 to -1 for individual puts. Delta is always a positive number for calls and a negative number for puts. The positive or negative nature of the sign is necessary to make the math come out right. Remember from 7th grade algebra that negative movement in price of the underlying times negative delta of a put gives a positive number. A call option with a delta of 0.5 would move up 50¢ for the first dollar increase in the price of the underlying. As an example consider the, with AAPL trading at $340/ share, the June 340 call with a delta of 0.5 would increase in value 50¢ as the price of AAPL traded up to $341. To put this concept in the framework more familiar to the stock trader, each individual share of long stock can be thought of to have a delta of one. Short stock has a delta of negative one. The delta of any individual option is not a constant value but increases and decreases as price of the underlying changes. Gamma represents the rate of change of delta as the strike price of an option moves closer to or farther from the current market price of the underlying. Gamma values for both puts and calls are positive. As an example, our June 340 AAPL call has a gamma of 2. As price moves from 340 to 341, delta will increase from 0.50 to 0.52. This dynamic nature of delta has the net result of a positive gamma position becoming increasingly long or short as price moves in the predicted direction. It is important to recognize that "position delta" is the sum of the delta of the various individual options within a position. It is derived from simply adding up all the individual deltas. To take a simple example, if I own one contract of my AAPL June 340 calls each with a delta of 0.50, I have a position delta of 100 options/contract * 0.5 deltas/option. When managing positions including multiple option legs with varying Greeks for each individual strategy, position deltas provide an important benchmark against which to measure potential adjustments and profit potential. Option strategies are often inscrutably complex. An important fundamental organizational concept is the ability to understand them in terms of their most basic structure. One of the hallmarks of options is their dynamic nature; nothing remains the same. Welcome to the world of the Greeks. |
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