Options Gamma

What is the greek called Gamma in options trading? How does options gamma affect my options trading?

Options Gamma - Definition

Options Gamma is the rate of change of options delta with a small rise in the price of the underlying stock.

Options Gamma - Introduction

Just as options delta measures how much the value of an option changes with a change in the price of the underlying stock, Options Gamma describes how much the options delta changes as the price of the underlying stock changes. Of the 5 options greeks, Delta and Gamma are the only ones that are related to each other and that Options Gamma is the only options greek that describes the change of another greek. That makes understanding options delta and Options Gamma extremely important to all options trading beginners.

Why Is Options Gamma Important?

Options Gamma is important because it affects the single options greek that determines the value of stock options most and that is the options delta. There is no question that options delta changes as it starts off at 0.5 when it is At The Money and then gradually move towards 1 as the options go deeper In The Money or gradually towards 0 as the options go farther Out Of The Money. The real question is, by what magnitude would the options delta change? Options Gamma measures that magnitude as well as the direction of change.

So, why is understanding the magnitude and direction of the change of options delta represented by its Gamma important?

Understanding Options Gamma is important for both directional and hedging trades. In directional trades, one would want an overall position Gamma to lean towards the direction of interest so that options delta expands as the trade develops. In hedging trades, one would want as low an overall options gamma as possible so that the options trading position remains as neutral to changes in the underlying stock as possible. Such hedging method has come to be known as Gamma Neutral Hedging.

Of course, if you are only buying call options or put options for a single directional trade, Options Gamma really have little to do with you because you can be sure that you are already buying positive Options Gamma which will increase the delta of your options as the stock rises or falls accordingly. Positive Options Gamma ensures that the delta of your options increases as it goes more and more in the money, increasing your profitability.

As such, Options Gamma is important to understand for options traders starting complex options strategies for the first time and for options traders who manage many complex options positions within a single portfolio like Market Makers do.

Options Gamma - Characteristics

Positive And Negative Polarity
Options Gamma come in positive or negative polarity. Positive Options Gamma suggests that the delta of the option will increase as the underlying stock rises. Negative Options Gamma suggests that the delta of the option will decrease towards -1 as the underlying stock rises.

Options Gamma & Options Moneyness
Options Gamma decreases towards 0 as the option moves deeper In The Money or farther Out Of The Money. At The Money options typically has the highest Options Gamma value. This also means that the delta value of Deep In The Money or Far Out Of The Money options are less likely to change with a small change in the price of the underlying stock.Learn about Options Moneyness now.

Options Gamma & Time
Options Gamma of At The Money options increases as expiration draws nearer while Options Gamma of both In The Money and Out Of The Money options decreases nearer to expiration.

Options Gamma & Directional Options Trading Positions

There are no questions that Options Gamma for a single long call or put options position is positive. This means that as those call or put options go more and more In The Money, their delta also increases towards 1. That is pretty straight forward. However, when you combine options into a complex options strategy, that relationship may be less obvious. There are directional options strategies that have positive delta but a negative overall options gamma. Such options trading strategies are meant to profit when the stock moves up a little but starts going into loss should the stock makes a huge move upwards as the delta reverses into negative due to the negative options gamma.

One example of such an options strategy is a Bull Ratio Spread. Bull Ratio Spreads have a positive delta value when first established but a negative overall options gamma value. As the stock rises, the overall value of that options trading position rises along with an erosion of the delta value due to the negative options gamma. As the stock continues to rise, it will come a point where the delta erodes to 0 and starts to turn negative. After that point, the position will start losing money as the stock rises.

When you are in a directional trade, which is when your options trading positions makes money only when the underlying stock goes in a certain direction, you want to make sure that the overall Options Gamma is positive so that the position will continue to profit as the stock moves further in the direction of your expectation. In general, positive Options Gamma is one which will move your initial delta value higher as the stock moves in your direction of expectation. Put options with negative delta value but positive options gamma will move towards a delta of -1 as the stock falls and call options with positive delta and gamma value will move towards a delta of 1 as the stock rises. Conversely, negative delta values work against your initial delta value as it erodes and reverses the polarity of your initial delta value as the stock moves in the direction of the initial delta's polarity.

Here's how you can expect your overall portfolio to behave with various delta/gamma combinations:

Positive Options Delta + Positive Options Gamma
The value of the overall options trading position will rise as the underlying stock rises. An example of such an options trading strategy is a Long Call.

Positive Options Delta + Negative Options Gamma
The value of the overall options trading position will rise at a decelerating rate as the underlying stock rises, coming to a point where the value of the overall position stagnants as the underlying stock rises and then starts losing money as the underlying stock continues to rise. There is therefore, a ceiling to the maximum profit possible with such a delta / gamma combination. An example of such an options trading strategy is a Bull Ratio Spread.

Negative Options Delta + Positive Options Gamma
The value of the overall options trading position will rise as the underlying stock falls. An example of such an options trading strategy is a Long Put.

Negative Options Delta + Negative Options Gamma
The value of the overall options trading position will rise at a decelerating rate as the underlying stock falls, coming to a point where the value of the overall position stagnants as the underlying stock falls and then starts losing money as the underlying stock continues to fall. There is therefore, a ceiling to the maximum profit possible. An example of such an options trading strategy is a Bear Ratio Spread.

Here's a table outlining the kind of options gamma that a position gains as different options are included:

Type	Delta value	Gamma Value
Long Call Option	Positive Delta	Positive Gamma
Short Call Option	Negative Delta	Negative Gamma
Long Put Option	Negative Delta	Positive Gamma
Short Put Option	Positive Delta	Negative Gamma

You would notice from above that shorting stock options always contributes negative Options Gamma regardless of whether call or put options.

It must be pretty confusing by now to remember the characteristics and relationships of options delta and options gamma. Here's an easy way of remember:

Positive Options Gamma makes delta more and more positive as the stock rises.

Negative Options Gamma makes delta more and more negative as the stock rises.

Options Gamma - Importance In Delta Neutral Hedging

There are many ways to achieve a Delta Neutral Position and may result in the overall position being positive or negative Options Gamma. In general, a delta neutral position with a positive Options Gamma will increase in value when the underlying stock goes up or down quickly, and that is the way most delta neutral positions are set up to do. An example of a delta neutral options trading strategy with positive Options Gamma is a Straddle. Delta Neutral Positions with negative Options Gamma would be better suited to profit from time decay through the Options Theta instead and will lose value if the underlying stock moves up or down quickly. An example of a delta neutral options trading strategy with negative Options Gamma is a Short Straddle. In both scenarios, as the position is delta neutral, its value would not change with small moves in the underlying stock. A fully hedged position which will not move with either big or small moves requires a Gamma Neutral Hedge.

Options Gamma - Relationship with Options Theta

Options Gamma is directly proportional to options theta. The higher the Gamma, the higher the Theta. High risk = high gains. High options gamma results in exponentially higher profits when the stock moves strongly but comes also with higher theta which decays the price of the option much faster. If that anticipated big move does not happen quickly, the option could lose a lot of money. Therefore, when one chooses such an aggressive option position, one must also take into consideration the higher risk involved due to higher Options Theta. Such balancing of potential risks over potential reward is actually prevalent in every aspects of options trading. There is never a free lunch.

Options Gamma Formula

Where...
d1 = Please refer to Delta Calculation
S = Current value of underlying asset
T = Option life as a percentage of year

Options Gamma Questions

:: "Can Options Delta Move Over 1 Due To Gamma?"