Option Greeks 101 – Delta, Gamma, Theta and Vega

by Mark S. Longo | July 26, 2010 1:29 pm

The world of options is dominated by four mathematical variables: delta, gamma, theta and vega. Collectively they are known as “the Greeks,” although options traders often add their own colorful adjectives when their P&Ls begin to sink.

What makes these four variables so important?

Taken together, they can provide an experienced trader with a comprehensive risk analysis in a single glance. Quite simply, if you want to trade options, then you have to master the Greeks.

Delta

Delta signifies the rate of change in an option’s price as it relates to movements in the underlying asset.

Most theoretical programs express an option’s delta as a number from 1-100. A delta of one indicates that an option will change its price by one cent for every one-dollar movement in the underlying. An option with a delta of a 100 will move in perfect correlation with the underlying.

Delta is an important variable because it shows the directional risk of an options position, as well as how many shares or futures are required to hedge that risk.

Delta also measures the probability of an option expiring in the money, but that is a discussion for another day.

Gamma

Options are not static instruments. Their characteristics and risks vary with fluctuations in the underlying asset. Gamma is used to measure the rate of change in delta as the underlying moves.

Gamma can be expressed as either a positive or a negative number. A positive gamma indicates that changes in delta will be positively correlated to movements in the underlying price. A negative gamma indicates that changes in delta will be inversely correlated to movements in the underlying price.

Theta

Theta is where things get confusing. Theta measures how much extrinsic value an option will lose every day until expiration. This steady erosion of value is also known as time decay.

Time decay is difficult to calculate accurately, and most theoretical models for theta break down around expiration.

Traders use theta to estimate the impact of time decay on their P&Ls.

Gamma and theta have an inverse correlation. A positive gamma position will lose money every day due to time decay, while a negative gamma position will collect money from time decay.

Vega

Vega is undoubtedly the king of all the Greeks. Vega measures the impact on an options price of a one-percent change in volatility. Since most option traders are actually volatility traders, understanding the intricacies of vega is crucial to long-term profitability.

DIY Greeks for the Retail Investor

Some of you out there might be wondering how to calculate your own Greeks.

Thankfully, there are a wide-variety of theoretical programs available for both retail and institutional customers. Which program is right for you depends on your understanding of options and the intricacy of your trading style.

If you are a retail customer, then your broker probably offers a free theoretical program. These programs range in quality from nearly useless to extremely powerful. In fact, the best retail offerings can often rival the professional theoretical programs on the market. The relentless march of technology has put a dazzling array of professional-grade tools in the hands of the average retail investor.

This article originally appeared on The Options Insider Web site[1].

Endnotes:
1. The Options Insider Web site: http://www.theoptionsinsider.com/

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