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8/14/2019 Option Greek - The Option Guide

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In options trading, you may notice the use of certain greek alphabets when describing risks associated with

various positions. They are known as "the greeks" and here, in this article, we shall discuss the four most

commonly used ones. They are delta, gamma, theta and vega.

1. Delta - Measures the exposure of option price to movement of underlying stock price

o What is delta and how to use ito Passage of time and its effects on the delta

o Changes in volatility and its effect on the delta

2. Gamma - Measures the exposure of the option delta to the movement of the underlying stock price

o What is gamma and how to use it

o Time and its effects on the gamma

o The relationship between the volatility and the gamma

3. Theta - Measures the exposure of the option price to the passage of time

o What is theta and how to use it

o Theta and time remaining

o Theta and volatility

4. Vega - Measures the exposure of the option price to changes in volatility of the underlying

o What is vega and how to use it

o Effects of time on the vega

http://www.theoptionsguide.com/the-greeks.aspx

DeltaThe option's delta is the rate of change of the price of the option with respect to its underlying

security's price. The delta of an option ranges in value from 0 to 1 for calls (0 to -1 forputs) and reflects

the increase or decrease in the price of the option in response to a 1 point movement of the underlying assetprice.

Far out-of-the-moneyoptions have delta values close to 0 while deep in-the-moneyoptions have deltas

that are close to 1.

Up delta , down delta

As the delta can change even with very tiny movements of the underlying stock price, it may be more

practical to know the up delta and down delta values. For instance, the price of a call option with delta of 0.5

may increase by 0.6 point on a 1 point increase in the underlying stock price but decrease by only 0.4 point

when the underlying stock price goes down by 1 point. In this case, the up delta is 0.6 and the down delta is

0.4.

Passage of time and its effects on the delta

As the time remaining to expiration grows shorter, the time value of the option evaporates and

correspondingly, the delta ofin-the-money options increases while the delta ofout-of-the-money options

decreases.

http://www.theoptionsguide.com/delta.aspxhttp://www.theoptionsguide.com/delta.aspx#delta-and-timehttp://www.theoptionsguide.com/delta.aspx#delta-and-volatilityhttp://www.theoptionsguide.com/gamma.aspxhttp://www.theoptionsguide.com/gamma.aspx#gamma-and-timehttp://www.theoptionsguide.com/gamma.aspx#gamma-and-volatilityhttp://www.theoptionsguide.com/theta.aspxhttp://www.theoptionsguide.com/theta.aspx#theta-and-timehttp://www.theoptionsguide.com/theta.aspx#theta-and-volatilityhttp://www.theoptionsguide.com/vega.aspxhttp://www.theoptionsguide.com/vega.aspx#vega-and-timehttp://www.theoptionsguide.com/the-greeks.aspxhttp://www.theoptionsguide.com/underlying-security.aspxhttp://www.theoptionsguide.com/underlying-security.aspxhttp://www.theoptionsguide.com/call-option.aspxhttp://www.theoptionsguide.com/put-option.aspxhttp://www.theoptionsguide.com/deep-out-of-the-money.aspxhttp://www.theoptionsguide.com/deep-out-of-the-money.aspxhttp://www.theoptionsguide.com/deep-in-the-money.aspxhttp://www.theoptionsguide.com/deep-in-the-money.aspxhttp://www.theoptionsguide.com/options-premium.aspx#time-valuehttp://www.theoptionsguide.com/delta.aspxhttp://www.theoptionsguide.com/in-the-money-option.aspxhttp://www.theoptionsguide.com/in-the-money-option.aspxhttp://www.theoptionsguide.com/out-of-the-money.aspxhttp://www.theoptionsguide.com/delta.aspx#delta-and-timehttp://www.theoptionsguide.com/delta.aspx#delta-and-volatilityhttp://www.theoptionsguide.com/gamma.aspxhttp://www.theoptionsguide.com/gamma.aspx#gamma-and-timehttp://www.theoptionsguide.com/gamma.aspx#gamma-and-volatilityhttp://www.theoptionsguide.com/theta.aspxhttp://www.theoptionsguide.com/theta.aspx#theta-and-timehttp://www.theoptionsguide.com/theta.aspx#theta-and-volatilityhttp://www.theoptionsguide.com/vega.aspxhttp://www.theoptionsguide.com/vega.aspx#vega-and-timehttp://www.theoptionsguide.com/the-greeks.aspxhttp://www.theoptionsguide.com/underlying-security.aspxhttp://www.theoptionsguide.com/underlying-security.aspxhttp://www.theoptionsguide.com/call-option.aspxhttp://www.theoptionsguide.com/put-option.aspxhttp://www.theoptionsguide.com/deep-out-of-the-money.aspxhttp://www.theoptionsguide.com/deep-in-the-money.aspxhttp://www.theoptionsguide.com/options-premium.aspx#time-valuehttp://www.theoptionsguide.com/delta.aspxhttp://www.theoptionsguide.com/in-the-money-option.aspxhttp://www.theoptionsguide.com/out-of-the-money.aspxhttp://www.theoptionsguide.com/delta.aspx8/14/2019 Option Greek - The Option Guide

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The chart above illustrates the behaviour of the delta of options at various strikes expiring in 3 months, 6months and 9 months when the stock is currently trading at $50.

Changes in volatility and its effect on the delta

As volatility rises, the time value of the option goes up and this causes the delta of out-of-the-money

options to increase and the delta ofin-the-moneyoptions to decrease.

The chart above depicts the relationship between the option's delta and the volatility of the underlying

securitywhich is trading at $50 a share.Next:Option Gamma

http://www.theoptionsguide.com/options-premium.aspx#time-valuehttp://www.theoptionsguide.com/options-premium.aspx#time-valuehttp://www.theoptionsguide.com/delta.aspxhttp://www.theoptionsguide.com/delta.aspxhttp://www.theoptionsguide.com/delta.aspxhttp://www.theoptionsguide.com/out-of-the-money.aspxhttp://www.theoptionsguide.com/in-the-money-option.aspxhttp://www.theoptionsguide.com/in-the-money-option.aspxhttp://www.theoptionsguide.com/underlying-security.aspxhttp://www.theoptionsguide.com/underlying-security.aspxhttp://www.theoptionsguide.com/underlying-security.aspxhttp://www.theoptionsguide.com/gamma.aspxhttp://www.theoptionsguide.com/gamma.aspxhttp://www.theoptionsguide.com/options-premium.aspx#time-valuehttp://www.theoptionsguide.com/delta.aspxhttp://www.theoptionsguide.com/out-of-the-money.aspxhttp://www.theoptionsguide.com/in-the-money-option.aspxhttp://www.theoptionsguide.com/underlying-security.aspxhttp://www.theoptionsguide.com/underlying-security.aspxhttp://www.theoptionsguide.com/gamma.aspx8/14/2019 Option Greek - The Option Guide

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GammaThe option's gamma is a measure of the rate of change of its delta. The gamma of an option is expressed

as a percentage and reflects the change in the delta in response to a one point movement of the underlying

stock price.

Like the delta, the gamma is constantly changing, even with tiny movements of the underlying stock price. It

generally is at its peak value when the stock price is near the strike price of the option and decreases as

the option goes deeper into or out of the money. Options that are very deeply into or out of the money have

gamma values close to 0.

Example

Suppose for a stock XYZ, currently trading at $47, there is a FEB 50 call option selling for $2 and let's

assume it has a delta of 0.4 and a gamma of 0.1 or 10 percent. If the stock price moves up by $1 to $48,

then the delta will be adjusted upwards by 10 percent from 0.4 to 0.5.

However, if the stock trades downwards by $1 to $46, then the delta will decrease by 10 percent to 0.3.

Passage of time and its effects on the gamma

As the time to expiration draws nearer, the gamma ofat-the-money options increases while the gammaof

in-the-moneyandout-of-the-money options decreases.

The chart above depicts the behaviour of the gamma of options at various strikes expiring in 3 months, 6

months and 9 months when the stock is currently trading at $50.

Changes in volatility and its effects on the gamma

When volatility is low, the gammaofat-the-moneyoptions is high while the gamma for deeply into or out-

of-the-money options approaches 0. This phenomenon arises because when volatility is low, the time value

of such options are low but it goes up dramatically as the underlying stock price approaches the strike

price.

http://www.theoptionsguide.com/at-the-money.aspxhttp://www.theoptionsguide.com/at-the-money.aspxhttp://www.theoptionsguide.com/gamma.aspxhttp://www.theoptionsguide.com/gamma.aspxhttp://www.theoptionsguide.com/in-the-money-option.aspxhttp://www.theoptionsguide.com/in-the-money-option.aspxhttp://www.theoptionsguide.com/out-of-the-money.aspxhttp://www.theoptionsguide.com/out-of-the-money.aspxhttp://www.theoptionsguide.com/gamma.aspxhttp://www.theoptionsguide.com/gamma.aspxhttp://www.theoptionsguide.com/at-the-money.aspxhttp://www.theoptionsguide.com/at-the-money.aspxhttp://www.theoptionsguide.com/options-premium.aspx#time-valuehttp://www.theoptionsguide.com/strike-price.aspxhttp://www.theoptionsguide.com/strike-price.aspxhttp://www.theoptionsguide.com/strike-price.aspxhttp://www.theoptionsguide.com/at-the-money.aspxhttp://www.theoptionsguide.com/gamma.aspxhttp://www.theoptionsguide.com/in-the-money-option.aspxhttp://www.theoptionsguide.com/out-of-the-money.aspxhttp://www.theoptionsguide.com/gamma.aspxhttp://www.theoptionsguide.com/at-the-money.aspxhttp://www.theoptionsguide.com/options-premium.aspx#time-valuehttp://www.theoptionsguide.com/strike-price.aspxhttp://www.theoptionsguide.com/strike-price.aspx8/14/2019 Option Greek - The Option Guide

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8/14/2019 Option Greek - The Option Guide

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The chart above illustrates the relationship between the option's theta and the volatility of the underlyingsecuritywhich is trading at $50 a share and have 3 months remaining to expiration

VegaThe option's vega is a measure of the impact of changes in the underlying volatility on the option

price. Specifically, the vega of an option expresses the change in the price of the option for every 1%

change in underlying volatility.

Options tend to be more expensive when volatility is higher. Thus, whenever volatility goes up, the price of

the option goes up and when volatility drops, the price of the option will also fall. Therefore, when calculating

the new option price due to volatility changes, we add the vega when volatility goes up but subtract it when

the volatility falls.

Example

A stock XYZ is trading at $46 in May and a JUN 50 call is selling for $2. Let's assume that the vega of the

option is 0.15 and that the underlying volatility is 25%.

If the underlying volatility increased by 1% to 26%, then the price of the option should rise to $2 + 0.15 =

$2.15.

However, if the volatility had gone down by 2% to 23% instead, then the option price should drop to $2 - (2 x

0.15) = $1.70

Passage of time and its effects on the vega

The more time remaining to option expiration, the higher thevega. This makes sense astime value makes

up a larger proportion of the premium for longer term options and it is the time value that is sensitive to

changes in volatility.

http://www.theoptionsguide.com/underlying-security.aspxhttp://www.theoptionsguide.com/underlying-security.aspxhttp://www.theoptionsguide.com/underlying-security.aspxhttp://www.theoptionsguide.com/vega.aspxhttp://www.theoptionsguide.com/vega.aspxhttp://www.theoptionsguide.com/options-premium.aspx#time-valuehttp://www.theoptionsguide.com/options-premium.aspx#time-valuehttp://www.theoptionsguide.com/underlying-security.aspxhttp://www.theoptionsguide.com/underlying-security.aspxhttp://www.theoptionsguide.com/vega.aspxhttp://www.theoptionsguide.com/options-premium.aspx#time-value8/14/2019 Option Greek - The Option Guide

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The chart above depicts the behaviour of the vega of options at various strikes expiring in 3 months, 6months and 9 months when the stock is currently trading at $50.