Option_Greeks_Delta_Gamma_Vega

8/7/2019 Option_Greeks_Delta_Gamma_Vega

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OPTIONGREEKSIn 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 it

O 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 itO 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

DELTA

The 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 forcalls (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 asset price.

Far out-of-the-moneyoptions have delta values close to 0 while deep in-the-money options 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 valueof the option evaporates and correspondingly, the

delta ofin-the-money options increases while the delta ofout-of-the-money options decreases.

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The chart above illustrates the behaviour of the delta 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 effect on the delta

As volatility rises, the time valueof the option goes up and this causes the delta ofout-of-the-moneyoptions to

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

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

which is trading at $50 a share.

GAMMA

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The 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 gammaofin-the-

money and out-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 gamma ofat-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.

When volatility is high, gamma tends to be stable across all strike prices. This is due to the fact that when volatility is

high, the time value of deeply in/out-of-the-money options are already quite substantial. Thus, the increase in the time

value of these options as they go nearer the money will be less dramatic and hence the low and stable gamma.

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The chart above illustrates the relationship between the option's gamma and the volatility of the underlying securitywhich is trading at $50 a share.

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 the vega. This makes sense as time value makes up a

larger proportion of the premium for longer term options and it is the time value that is sensitive to changes involatility.

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

THETA

The option's theta is a measurement of the option'stime decay. The theta measures the rate at which options lose

their value, specifically the time value, as the expiration date draws nearer. Generally expressed as a negative

number, the theta of an option reflects the amount by which the option's value will decrease every day.

Example

A call option with a current price of $2 and a theta of -0.05 will experience a drop in price of $0.05 per day. So in two

days' time, the price of the option should fall to $1.90.

Passage of time and its effects on the theta

Longer term options havetheta of almost 0 as they do not lose value on a daily basis. Theta is higher for shorter term

options, especially at-the-moneyoptions. This is pretty obvious as such options have the highest time value and thus

have more premium to lose each day.

Conversely, theta goes up dramatically as options near expiration as time decay is at its greatest during that period.

Changes in volatility and its effects on the theta

In general, options of high volatility stocks have highertheta than low volatility stocks. This is because the time value

premium on these options are higher and so they have more to lose per day.

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

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Option_Greeks_Delta_Gamma_Vega