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Option Greeks Explained

Updated on August 11, 2011

NOTE: I can't figure out how to put pictures inside the text so I'm just putting them at the top instead of the bottom because I don't want you to think that I forgot to put in the graphs. If anybody could leave a comment below and tell me how to put the graphs in the text that would be greatly appreciated

Delta with the passage of time
Delta with the passage of time
Delta with different implied volatilities
Delta with different implied volatilities
Gamma with the passage of time
Gamma with the passage of time
Vega with the passage of time
Vega with the passage of time
Theta with the passage of time
Theta with the passage of time
Theta with different volatilities
Theta with different volatilities
Rho with the passage of time
Rho with the passage of time
Rho with the passage of time
Rho with the passage of time


Key:

OTM = Out of the money (hasn't reached strike price, no intrinsic value, only extrinsic value)

ATM = At the money (has just reached the strike price)

ITM = In the money (has past the strike price, has intrinsic value, can be exercised for a profit)

Positive = Long (When I say you are ABC positive it basically means you are long ABC)

Negative = Short (When I say you are ABC negative it basically means you are short ABC)


Option Greeks Explained

Trading options is risky business because not online does it provide huge leverage but it is also exposed to many other risks besides directional movement of the underlying instrument. If you can learn about each variable and how it works you can minimize your risk while potentially raising your profit potential.

Learning about the Greeks will be the most beneficial to option traders who trade options with the intention of selling it back later (and not exercising it) because all of the Greeks effect the price of the option. This doesn't mean that traders who intend to exercise it will not benefit, they should still learn about the Greeks because it can tell the trader whether he/she is overpaying for certain options (this actually has more to do with an option pricing model rather than the Greeks).

There are five Greeks:

1. Delta

2. Gamma

3. Gamma of Gamma

4. Vega

5. Theta

6. Rho

One thing to note is that all Greeks due not stay constant! They change due to the passage of time, changes in implied volatility, and movement of underlying instrument!

Delta

Delta is basically how much the price of option moves due to a 1 point move in the underlying instrument. For example

Stock XYZ: 55$

XYZ Call: 5$

if the stock moved up by one point:

Stock XYZ: 56$

and the call moved up by .50$:

XYZ Call: 5.50$

That would mean that the call had a delta of .5 (this actually isn't the "mathematically correct" way to do it, but it's easier)

The delta of call options will always be shown as positive and the delta of put options will always be shown as negative. This means if you buy a call option, you will be delta positive (meaning you want the underlying to go up), if you sell a call option, you will be delta negative (meaning you want the underlying to go down). If you buy a put option, you will be delta negative (meaning you want the underlying to go down), if you sell a put option, you will be delta positive (meaning you want the underlying to go up).

Some important things to know about delta is how it changes due to the passage of time, changes in implied volatility, and movement of underlying instrument. Here are two graphs, the first one shows delta if the underlying instrument moved and how delta is effected by the passage of time, the second one shows delta if the underlying instrument moved and how delta is affected by changes in implied volatility.

This chart shows a couple of things.

1. When an option is OTM, its delta will be less than .50

2. When an option is ATM, its delta will be around .50 (when it gets nearer to expiration, it will usually be a little above .50)

3. When an option is ITM, its delta will be over .50

4. As time passes, OTM options will have their delta move toward 0 and ITM options will have their delta move toward 100.

This chart shows:

1. When Implied volatility decreases, OTM options will have their delta move toward 0 and ITM options will have their delta move toward 100. Does this sound familiar? One thing to remember is that changes in implied volatility in many cases will change the Greeks the same way the passage of time does.

Green = 110% Implied Volatility

Orange = 80% Implied Volatility

Red = 50% Implied Volatility

Yellow = 20% Implied Volatility

(This was done for a 1 month option)

Gamma

Gamma is how much the delta changes when the underlying moves by one point. For example:

Stock XYZ: 55$

XYZ Call's Delta: .4 (Different option from last scenario)

Then the stock moves up one point to:

Stock XYZ 56$

XYZ Call's Delta: .45

That would mean the gamma of the call is .05 (this actually isn't the "mathematically correct" way to do it, but it's easier)

Gamma is always shown as positive. If you buy a call option or a put option, the gamma will be positive (meaning you want the underlying to move a lot in one (or either) direction), if you sell a call option or a put option, the gamma will be negative (meaning you want the underlying to stay relatively still).

This chart shows:

1. The gamma of an option is at its peak when the strike price is the same as the underlying price (AKA: At the money)

2. Gamma of an option has sharper changes due to change of underlying price when there isn't as much time until expiration

3. Since gamma has sharper changes due to change of underlying price when there isn't a lot of time until expiration, we can assume that whenever there is low implied volatility, the gamma will also have sharper changes (I swear I'm not being lazy, I just can't find a graph of gamma when there is implied volatility changing D:)

Gamma of gamma

Gamma of gamma isn't actually one of the "official Greeks) and isn't part of most options trading software or option calculators so we won't be going over it a lot.

It is how much gamma changes due to a one point move in the underlying instrument. For example:

Stock XYZ: 55$

Call Gamma:.05

Then the stock moves up one point to:

Stock XYZ 56$

Call Gamma: .06

This option has a gamma of gamma of .01

This Greek is usually used by professional traders who trade in huge quantities.

Vega

Vega is how much the price of an option changes due to changes in implied volatility. For example:

Implied volatility on a call: 35%

Call Price: 3$

Then the implied volatility of the call moves up one point to:

Implied volatility on the call: 36%

Call Price 3.30$

The vega would .30

Vega is always shown as positive. If you buy a call option or a put option, the vega will be positive (meaning you want the implied volatility to go up), if you sell a call option or a put option, the vega will be negative (meaning you want the implied volatility to go down).

This chart shows:

1. The vega of an option is at its peak when the strike price is the same as the underlying (AKA: At the money)

2. Vega of options with a longer time to expiration are greater than vega of options with a shorter time to expiration.

3. Since vega of options with a longer time to expiration are greater than vega of options with a shorter time to expiration, we can assume that whenever there the vega of high implied volatility option will be greater than vega of lower implied volatility options.

Theta

Theta is how much the price of an option changes due to a 1 day passage of time. For example:

Call price today is 3$

Call price tomorrow is 2.98$

Theta is .02

Theta is always shown as negative. If you buy a call option or a put option, theta will be negative (meaning you don't want time to pass. There is actually an exception to this rule*) If you sell a call option or a put option, theta will be positive (meaning you do want time to pass).

These charts show:

1. Theta is highest when the option is ATM

2. Theta will rapidly increase around the 1 month period (meaning at 1 month, you will start losing/gaining a lot more due to the passage of time than you previously did)

3. The relationship between implied volatility and passage of time will actually be a little different for this one. Theta will actually be HIGHER when implied volatility is higher because of the fact that when there is high implied volatility, there will be a lot of extrinsic value (or at least more than if there was a low implied volatility) and since that extrinsic value has to decline to 0 in the same amount of time if there were a low implied volatility, you will be losing more money per day.

*Whenever an option is extremely deep ITM, sometimes it will have negative extrinsic value (due to having too much intrinsic value) and buying it, you will actually have a positive theta meaning you want time to pass. This isn't that helpful though because you could just exercise it and take the same amount of profit you would if you had just waited. Also there won't be many of these situations due to arbitrageurs. This may seem a bit confusing so if you have any questions, just ask.

Rho

Rho is how much the price of an option change due to a 1% move in interest rates.

Risk free interest rate: 1%

Call Price: 3$

Then the risk free interest rate moves up by 100 basis points

Risk free interest rate: 2%

Call Price: 3.01$

This option has a rho of .01

The rho of call options will always be shown as positive and the rho of put options will always be shown as negative. This means if you buy a call option, you will be rho positive (meaning you want the risk free interest rate to go up), if you sell a call option, you will be rho negative (meaning you want the risk free interest rate to go down). If you buy a put option, you will be rho negative (meaning you want the risk free interest rate to go down), if you sell a put option, you will be rho positive (meaning you want the risk free interest rate to go up).

This chart shows:

1. The rho of long term options is greater than the rho of shorter term options.

2. Since the rho of long term options is greater than the rho of shorter term options, you can assume the rho of high implied volatility options is greater than the rho of low implied volatility options.



Okay well that pretty much covers all of the Greeks. I'm not the best at explaining things so if you are confused, feel free to ask me to clarify (my e-mail is whua0000@gmail.com if you'd rather me do it privately).

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