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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.aspx
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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.aspx
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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.aspx
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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-value
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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.
