Blessed Are The Greeks

The ancient Greeks are justly praised for inventing much of elementary mathematics. But it was left to moderns to create the tools that help options traders quantify risk and calculate prices. Chief among these tools are several quantities known fondly as The Greeks: delta, theta, gamma and vega.

While the underlying mathematics is heavy going, the basic concepts are simple and can be used by any trader to help measure risk and maximize profits.

The Greeks are based on factors that common sense would suggest affect the price of an option. The determinants are the underlying asset's market price, the option strike price, the time left to expiration, volatility and short-term interest rates. All these pieces of data are readily available and it's clear why they would affect an option's value.

Take the strike price for example. That's the contractually specified price at which the asset, say a stock, would have to be bought or sold if the option were exercised.

Suppose MSFT (Microsoft) were selling at $28 per share and the option considered was a June 31 call. (Note: the '31' refers to the strike price, not the date on which the option expires.) This option is 'out-of-the-money' since the strike price is higher than the current market price.

Clearly, the price of the option itself (the 'premium') will be affected by just how far out-of-the-money the option is. One measure of this difference is the first Greek: delta.

Not a simple difference, the delta is a ratio which compares the change in price of the asset to the change in price of the option. For example, if the delta in the above example were 0.7, for every $1 rise in MSFT the call option can be expected to increase by 70 cents ($0.70).

A trader doesn't need to know how to calculate it, only how to use it. (Any good options trading software will show all four Greeks, along with price, expiration, etc.) Delta tends to increase the closer the option is to expiration for those close to in-the-money. Delta is also affected by changes in implied volatility. (The latter is also frequently provided by trading software.)

Theta measures what is sometimes referred to as the 'time decay' of an option. Since all have an expiration date, and since the less time left the less likely the market price will move in a desired direction, theta is a measure of risk and value.

Suppose that MSFT June 31 call were priced at $3 and the theta were 0.5. Then, in theory, the value of the option would drop by 50 cents ($0.50) per day.

As expiration nears, the price for a premium can be expected to decline at a faster rate. An option with, say, two days left is losing value quicker than one with three months remaining. That change is reflected in the value of theta.

Next in line is gamma. Here again the mathematics is slightly advanced, but the idea is simple. (For those who remember some college calculus, gamma is a function of the first derivative of delta.)

Gamma measures the rate of change of delta with respect to changes in the price of the underlying asset. Gamma is helpful when trying to estimate the price of an option relative to the degree it's in or out of the money.

When an option is far in or out of the money, gamma is small. When the option price approaches 'at-the-money', gamma is a maximum.

Last, we look at vega. Vega measures the sensitivity of the price of an option to changes in volatility. Volatility is the frequency with and degree to which a price changes. When prices rise or fall sharply, volatility is high.

(Volatility is yet another 'Greek', beta. Mathematicians and traders both are restless and ever-curious people, so there are actually several kinds of volatility. Implied volatility, for example, is determined by exercise price, rate of return, maturity date and premium. Historical volatility is another commonly charted item.)

The calculations are complex, but again the idea is simple. Risk increases as volatility rises, because risk is all about uncertainty and potential loss or gain.

If the price changes slowly, investors have time to react. If the price changes by an extremely small amount, there is little to lose or gain. Both factors are important in measuring risk. A highly volatile instrument experiences large swings in price in short periods of time.

Vega is one helpful measure for quantifying that volatility and making trading decisions. Any increase in volatility in an underlying asset, will tend to show up as an increase in the price of an option. Individual options vary in the amount of their reaction to volatility, though, and so different options have different vegas.

Keep in mind that all these pieces of data, though useful and arrived at by complex mathematical formula, are at bottom guesses. Educated guesses, to be sure, but nevertheless estimates in an inherently uncertain market. All are based on various models of how options prices and the assets underlying these derivatives may behave in the future. Those models are, as their proponents will agree, not exact predictions.

The two most common are perhaps the Blacks-Scholes model and the Binomial model. There's no need here to display these elegant but intimidating formulae. The savvy trader need only remember that the data should be used as part of an overall strategy of research, not as a substitute for research.

Acquire the software needed to display these figures, along with several other useful ones, and look for trends. Even short term traders (as options traders tend to be) need to examine past long-term trends before placing their bets.

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