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Greeks A variety of Greek letters are used in describing characteristics of options. It is important to understand these terms when trading options. Below you will find some definitions of the most important Greeks.
DeltaDelta is by far the most important Greek term used in the options arena. Simply put, Delta is a measure of the price-change relationship between an option and the underlying futures.
When trading outright futures, the Delta is very simply the number of futures you are long or short. For example, if you are long 5 gold futures contracts, the Delta of your position is +5, which means that if gold goes up 2 points, you simply multiply 5 x 2 = 10 to realize that your position has increased in value by 10 points.
When trading options or a combination of options and futures, an understanding of Delta and how it is calculated becomes important.
Let us first take a look at how the Delta is calculated for one particular option. The Delta of an option is a positive or negative number between 0 and 1.
An at the money option always has a Delta of .5 or -.5. For instance, if the price of gold is $600, and you buy one 600 call option, the Delta on that option is .5. This means that if gold goes up $10, the value of the option should increase by 10 x .5 = $5.
A deep in the money option has a Delta that approaches 1 or 1. This means that a deep in the money option acts very similarly to a futures contract. For instance, if the price of gold is $600, and you own a $500 call that is deep in the money, the Delta on that call might be .95. Therefore if gold goes up $10, you might expect the option to increase by $9.50.
A deep out of the money option has a Delta that approaches 0. This means that a movement in the underlying futures contact might have little effect on the option's value. For instance, if gold is $600, and you own a $700 call, the Delta on that call might be .05. Therefore if gold goes up $10, you might expect the option to increase by only $.50.
For practical use, when one has a position in a particular market that combines futures with long and short puts and calls, it is important to know the Delta of the overall position in order to understand how a movement in the underlying futures will affect one's profit or loss on the position.
Gamma Gamma is the rate at which an option's Delta changes as the underlying future price changes. Gamma is calculated by dividing the change in Delta by the change in the underlying futures price. It measures the change in Delta caused by the change in the underlying futures price. Options that are very deep in the money or very deep out of the money will tend to have lower Gammas than options that are near the money.
Rho Rho indicates the sensitivity of an option’s price to changes in interest rates. Rho is the expected change in an option’s theoretical value for a one percent change in interest rates. When interest rates change, call and put values can be positively or negatively affected. Higher interest rates have a positive effect on the value of calls and a negative effect on the value of puts. Calls have positive rho, and puts have negative rho. For example, a call with a rho of +0.09 will gain $0.09 with each one-percentage-point rise in interest rates and fall $0.09 with each one-point fall in interest rates. A put with a rho of -0.09 will lose $0.09 with each one-point rise in interest rates and gain $0.09 in value with a one-point fall in interest rates. Also, because the effect of interest is greater over a greater time period, the longer the time to expiration, the larger value (positive or negative) rho will have.
Theta Theta is the Greek letter used to measure the change in an option's premium caused by the passing of time. Theta measures the rate of time value decay, and it accelerates as the option's expiration date nears.
Vega Vega measures the rate of change of an option's premium for an equivalent change in volatility in percentage terms. In other words, Vega tells you how much an option's value changes given a 1% change in volatility. If implied volatility falls by 1%, then Vega is the percentage drop in an option's premium value. The formula to compute Vega is the percentage change in premium divided by the percentage change in volatility.
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