Option Greeks: GAMMA

Gamma measures the rate of change of delta due to a one-point change in the price of the underlying stock. In other words, Gamma estimates how much delta would change if the price of the underlying stock changes by $1. So, gamma can tell you how “stable” your delta is. A big gamma means that your delta can start changing considerably for even a small move in the stock price.
Unlike delta, gamma is always positive for both Calls and Puts.

Example:
ABC Jun 60 Call has a delta of +0.25 and ABC Jun 60 Put has a delta of -0.75. The current ABC stock price is 50. The gamma for both the ABC Jun 60 Call and Put is 0.03.
If the stock increases by $1 from $50 to $51, the delta of ABC Jun 60 Call will become +0.28 [= +0.25 + ($1 * 0.03)], and the delta of ABC Jun 60 Put becomes -0.72 [= -0.75 + ($1 * 0.03)].
If the stock falls by $1.00 to $49, the delta of ABC Jun 60 Call becomes +0.22 [= +0.25 + (-$1 * 0.03)], and the delta ABC Jun 60 Put becomes -0.78 [= -0.75 + (-$1 * .03)].

Gamma and the position in the market:
* Both long calls and long puts always have positive gamma.
* Both short calls and short puts always have negative gamma.
* Stock has zero gamma because its delta is always 1.00 – it never changes.

Initially, it was quite hard for me to understand why “both long calls & long puts always have positive gamma” and “both short calls and short puts always have negative gamma”. Until I drew a “delta ruler” (see picture below) which could really help me to understand the above concepts.



Now, I’ll try to elaborate more on how this “ruler” has helped me to understand Gamma concepts.
Before we start, let’s refresh the concepts we discussed earlier in “Delta – Part 1”:
* Long calls have positive delta; short calls have negative delta.
* Long puts have negative delta; short puts have positive delta.

POSITIVE GAMMA means the delta will increase when the underlying stock price increases, and will decrease when the stock price decrease (positive relationship).

What does “long calls have positive gamma” mean?
Since the delta of long calls is positive, when the stock price rises, the delta of long calls will increase, i.e. it becomes more positive and moves towards +1.
In contrast, when the stock price falls, the delta of long calls will decrease, whereby it becomes less positive and moves towards 0.

And what does “long puts have positive gamma” mean?
Since the delta of long puts is negative, when the stock price rises, the delta of long puts will increase, whereby it becomes less negative and moves towards 0.
On the other hand, when the stock price falls, the delta of long puts will decrease, meaning that it becomes more negative and moves towards -1.

NEGATIVE GAMMA means the delta will decrease when the underlying stock price rises, and will increase when the stock price drops (negative relationship).

What does “short calls have negative gamma” mean?
Since the delta of short calls is negative, when the stock price rises, the delta of short calls will decrease, i.e. the delta becomes more negative and moves towards -1.
On the other hand, when the stock price falls, the delta of short calls will increase, whereby the delta becomes less negative and moves towards 0.

What does “short puts have negative gamma” mean?
Since the delta of short puts is positive, when the stock price rises, the delta of short puts will decrease, whereby the delta becomes less positive and moves towards 0.
On the contrary, when the stock price falls, the delta of short puts will increase, i.e. the delta becomes more positive and move towards 1.

Gamma of ATM, ITM & OTM Options
Gamma is the largest for the At-The-Money (ATM) options, and gradually gets lower as it moves furthers towards In-The-Money (ITM) and Out-Of-The-Money (OTM). This means that the delta of ATM options changes the most when the stock price moves up or down, as compared to ITM & OTM options.
Hence, practically speaking, an ATM Call can provide a good balance of potential profit if the stock rises versus loss if the stock falls. An OTM Call will not make as much money if the stock price increases, and an ITM will lose more money if the stock price drops.

To read about other Option Greeks, go to: Option Greeks.

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* OPTION PRICING: How Is Option Priced?
* Understanding Implied Volatility (IV)
* Difference Between Option’s Volume and Open Interest
* Options Trading Basic – Part 2

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Option Greeks: DELTA (Part 3)

Go back to “Delta - Part 2”.

Although some people may not be totally agreeable, there is another way how we can “interpret” Delta.
Options Guy’s Blog posted an article about another “definition” of delta:
”Delta is the probability of the option contract being in-the-money at expiration”.

I agree that this is not the theoretical definition of Delta. I still use delta data as per the theoretical definition, i.e. how much the option’s theoretical value will change when the stock price changes by $1.
But I do feel that the other “definition” of delta has helped me to understand more about some “behavior” of delta.

For instance:

Why for ITM options, for the same strike price, the longer days to expiration, the lower the delta?
Because ITM option with more days to expiration has more time to move.
Options Guy argues that “more time to move means less likelihood of the option still being in-the-money at expiration; this translates into a smaller Delta”.

And why for OTM options, for the same strike price, the longer days to expiration, the higher the delta?
Options Guy argues that “if you’re buying OTM options, you need time for the stock to move up to the strike price. In other words, there’s a much higher probability of the underlying finishing ITM for the [longer to expiration] option than for the [nearer to expiration option]; Delta reflects that probability”.

Likewise, we can also use the same logic to answer this question:
Why a decrease in volatility will push the deltas of ITM Calls closer to 1 (-1 for Puts) and the OTM options’ delta closer to 0.
Because decreased (implied) volatility means the future stock price fluctuation is expected to be lower. As a result, for ITM options, the probability of the options to be still in-the-money at expiration will be higher, which translates into a higher Delta.
On the other hand, for OTM options, decreased (implied) volatility would lower their probability to be in-the-money at expiration. And the lower delta reflects that probability.

Hope this can help you to better understand Delta too. :)

To read about other Option Greeks, go to: Option Greeks.


Related Topics:
* Trading Educational Videos You Should Not Miss
* OPTION PRICING: How Is Option Priced?
* Options Trading Basic – Part 2
* Difference Between Option’s Volume and Open Interest

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Option Greeks: DELTA (Part 2)

Go back to “Delta - Part 1”

Factors That Affect Option’s Delta
There are a few factors that influence option’s Delta:

a) How close or how far away the stock price from the strike price.
At-the-money (ATM) options have deltas around 0.5; Out-of-the-money (OTM) options have deltas between 0 to 0.5; In-the-money (OTM) options have deltas between 0.5 to 1. (The delta values will be positive for Calls & negative for Puts).
When options are deep OTM, they have a small delta, because changes in the stock price will lead to only small changes in the option price. But as the options move towards in the money resulting from a continued rise in the stock price, the delta gets larger.

As the stock price moves and an option gets deeper ITM, delta will change and would be approaching 1 for Call and –1 for Put. When the delta is near 1 for Call or -1 for Put, the options will begin to trade like a stock, moving almost dollar for dollar with the stock price. This occurs with little or no time value, as most of the value of the option is intrinsic.

Example:
ABC stock is currently trading at $50. The price of May 50 Call option (ATM option) is $3. The ATM option’s delta is 0.5. If the stock rises by $1 from $50 to $51 (all other factors unchanged), the option price will theoretically increase by $0.5 from $3 to $3.5. So, if we own one contract (long position), we will gain $50 (=0.5 x 100 shares/contract).
Now, if the stock rises $1 further from $51 to $52, will the option price move $0.5 again, or more or less than that? The answer is more than $0.5. Because when the stock was trading at 51, the option’s delta should be about 0.60, so when the stock made another $1 move, the option price will increase $0.6, from $3.5 to $4.1.

b) Changes in volatility and time to expiration.
Changes in volatility or time to expiration will change delta. Even though the stock price does not move, delta will change when there are changes in volatility or time to expiration.
However, for ATM options, the delta is relatively unaffected to changes in volatility or time to expiration. This means both ATM options with 90 days and 30 days to expiration will have deltas close to 0.5 (Assuming other factors constant).

In contrast, for ITM & OTM options, the more ITM or OTM an option is, the more sensitive its delta is to changes in volatility or time to expiration.
Fewer days to expiration or a decrease in volatility will push the deltas of ITM Calls closer to 1 (-1 for Puts) and the OTM options’ delta closer to 0.

The Impact of Time Remaining To Expiration on Delta
An option’s Delta does change as one trading day passes. This is often called as “Delta Decay”.
As the expiration is nearing (time to expiration gets shorter), the time value portion of an option is declining (time decay effect). This causes the delta of ITM options to increase (i.e. ITM option’s delta gets closer to 1 for Calls or to -1 for Puts) and the delta of OTM options to decrease (i.e. OTM option’s delta gets closer to 0).

As a result:
For ITM options, for the same strike price, the longer days to expiration, the lower the delta. Hence, a next month ITM option will have a lower delta than the current month option.
On the other hand, for OTM options, for the same strike price, the longer days to expiration, the higher the delta. So, a next month OTM option will have higher delta than the current month option.

The Impact of Implied Volatility (IV) on Delta
When volatility increases, the time value portion of the option will rise. As a result, the delta of OTM options goes up, whereas the delta of ITM options goes down.

c) Changes in stock price.
The option’s delta changes when the stock price changes. The sensitivity of delta to the movement of the stock price is measured by Gamma.

Continue to “Delta - Part 3”.

To read about other Option Greeks, go to: Option Greeks.

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* Options Trading Basic – Part 1
* Options Trading Basic – Part 2
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Option Greeks: DELTA (Part 1)

What is Delta?
Delta is a measure of the change in the option’s price resulting from a change in the underlying stock price. It estimates how much the theoretical value of option price will change when the price of the underlying stock changes by $1, assuming all other variables are unchanged.

Positive delta means that the option’s value will increase when the underlying stock price increases, and will decrease when the stock price decreases (positive relationship).
Negative delta means that the option’s value will increase when the underlying stock price drop, and will decrease when the stock price rises (negative relationship).

For Calls, the value of delta ranges from 0 to 1, whereas for Puts from -1 to 0.
Calls have a positive delta because Call premiums increases when the underlying stock price increases, and vice versa, assuming all other factors remain the same.
In contrast, Puts have a negative delta because the Put option price drops when the stock price goes up, and vice versa.

It is interesting to note that for every Strike Price in the Option Chain, if you add the absolute values of delta of Call & Put, the sum will always be 1.
For example, the delta of ABC Jun 60 Call is 0.25 and the delta of ABC Jun 60 Put is -0.75. The sum of their absolute values is: ¦0.25¦ + ¦-0.75¦ = 1.

Delta and the position in the market:
· Long calls have positive delta; short calls have negative delta.
· Long puts have negative delta; short puts have positive delta.
· Long stock has positive delta; short stock has negative delta.

Continue to “Delta - Part 2”.

To read about other Option Greeks, go to: Option Greeks.

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* Options Trading Basic – Part 1
* Options Trading Basic – Part 2
* Understanding Implied Volatility (IV)
* Getting Started Trading
* FREE Trading Videos from Famous Trading Gurus

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OPTION GREEKS - Introduction

The "Greeks" in options trading is known as a way to measure the sensitivity of an option price to changes in its parameters. The Greeks can help option traders to better understand the potential risk and reward of an option position. However, it is important to note that the numbers given for each of the Greeks are strictly theoretical, as they are only projected based on mathematical models.

In addition, the Greeks numbers also change as the conditions (like actual stock price, volatility) change. How the various Greeks move as conditions change depends on how far the strike price is from the actual price of the stock (Deep ITM or ATM or deep OTM) and how much time is left until expiration.

Options Greeks numbers are usually presented in Greeks tables. The numbers shown in the Greeks table are normally in decimals that indicate the change per share. To normalize the Greeks for dollars, just multiply them by 100 (the number of shares per option contract).

Samples of Greeks Tables for Call Options:













Samples of Greeks Tables for Put Options:

The following are the major Greeks in options trading:

1. Delta
Delta is a measure of the change in the option price resulting from a change in the underlying stock price.

2. Gamma
Gamma is a measure the rate of change of delta due to a one-point change in the price of the underlying stock.

3. Theta
Theta is a measure of the rate of decline of option’s time-value resulting from the passage of time (TIME DECAY).

4. Vega
Vega is a measure the sensitivity of an option’s price to changes in Implied Volatility (IV).

5. Rho
Rho is a measure of the change in an option's price due to a change in interest rate.

We’ll discus each of the Greeks further in the next posts.

To read further about each of the Option Greeks, go to: Option Greeks.

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* Difference Between Option’s Volume and Open Interest
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