Gamma and Option Risk

Gamma Is Not the Same for Every Option

We know that Gamma measures the rate of change of Delta.

But Gamma itself varies across different Strike Prices.

For Call and Put Options:

Gamma is always positive.
ATM options generally have the highest Gamma.
ITM and OTM options generally have lower Gamma.
Delta changes most rapidly when the option is around ATM.

This makes the Strike Price an important factor when assessing Gamma risk.

Gamma Across Different Strikes

Consider three Call Options:

ITM Call
ATM Call
OTM Call

As the underlying price moves, all three options experience changes in Delta.

However, the ATM option experiences the fastest change in Delta because its Gamma is highest.

The ITM and OTM options generally have lower Gamma, so their Delta changes more slowly.

This can be understood simply as:

ATM → Highest Gamma → Faster Delta Change

ITM / OTM → Lower Gamma → Slower Delta Change

Why Does High Gamma Matter?

High Gamma means that Delta can change quickly when the underlying moves.

Suppose an option initially has a Delta of 0.50.

If its Gamma is high and the underlying moves significantly, Delta can move substantially away from 0.50.

This means the position's directional exposure can change much faster than expected.

For an option buyer, this can work in their favour when the underlying moves in the expected direction.

For an option seller, the same rapid change in Delta can increase risk significantly.

Long Gamma and Short Gamma

The Gamma position depends on whether you have bought or sold the option.

Buying Options = Long Gamma

When you buy a Call or Put Option, you are Long Gamma.

If the underlying moves, the changing Delta can increase your exposure in the direction of the market movement.

Selling Options = Short Gamma

When you sell a Call or Put Option, you are Short Gamma.

A sharp move in the underlying can make the position's Delta change rapidly, increasing directional risk.

This is one reason why option sellers need to pay close attention to Gamma.

Gamma and Risk Management

Consider a trader who has defined a maximum directional exposure for an option position.

Initially, the position may appear to be within that limit.

But if the trader is short an option with high Gamma and the underlying moves sharply against the position, Delta can increase quickly.

The position may therefore become much larger in directional terms than it originally appeared.

Simple Example

Suppose:

Position Delta = 0.50
Gamma = 0.005
Underlying moves by 70 points

Change in Delta:

0.005 × 70 = 0.35

New Delta:

0.50 + 0.35 = 0.85

The position has therefore become significantly more sensitive to further price movements.

This illustrates why Gamma can change risk even when the number of contracts has not changed.

Gamma and the Direction of the Move

Gamma is positive for both Calls and Puts.

However, the change in Delta depends on the option type and the direction of the underlying movement.

For example, consider an ATM Put with:

Delta = -0.50
Gamma = 0.004

If the underlying rises by 10 points:

Change in Delta:

0.004 × 10 = 0.04

New Delta:

-0.50 + 0.04 = -0.46

If the underlying falls by 10 points:

Change in Delta:

0.004 × (-10) = -0.04

New Delta:

-0.50 − 0.04 = -0.54

So Gamma helps explain how the Put's Delta moves as the underlying changes.

Gamma and Time to Expiry

Gamma also behaves differently depending on the time remaining until expiry.

When there is plenty of time remaining:

Gamma is generally lower.
ITM, ATM and OTM options tend to have relatively moderate Gamma.

As expiry approaches:

ITM and OTM Gamma tends to move towards zero.
ATM Gamma can increase sharply.
ATM options become particularly sensitive to changes in the underlying.

This is why high-Gamma ATM options close to expiry require special attention.

Why ATM Options Need Special Attention

The combination of ATM status and approaching expiry can create particularly high Gamma.

This means a relatively small movement in the underlying can cause a meaningful change in Delta.

For option sellers, this can quickly increase directional exposure.

Therefore, traders should be especially careful when shorting options with high Gamma, particularly around ATM and close to expiry.

Practical Insight

Gamma should not be viewed in isolation.

When analysing an option position, consider:

Current Delta
Gamma
Strike Price
Time to Expiry
Direction of the underlying

A position with a manageable Delta today can become much more sensitive tomorrow if Gamma is high.

Common Beginner Mistake

A common mistake is looking only at the number of option contracts to judge risk.

Ten option contracts may appear manageable based on their current Delta.

But if those options have high Gamma, a significant market move can rapidly increase the Position Delta and therefore the directional exposure.

Key Insight

Delta tells you how sensitive the option is. Gamma tells you how quickly that sensitivity can change.

High Gamma can be especially important for option sellers because their directional exposure can increase rapidly when the market moves against them.

Key Takeaways

Gamma measures the rate of change of Delta.
Gamma is positive for both Call and Put Options.
ATM options generally have the highest Gamma.
ITM and OTM options generally have lower Gamma.
High Gamma means Delta can change rapidly when the underlying moves.
Buying options creates a Long Gamma position.
Selling options creates a Short Gamma position.
Short Gamma positions can become significantly riskier when the underlying moves sharply.
Gamma can become particularly high for ATM options as expiry approaches.
ITM and OTM Gamma generally moves towards zero near expiry.
Traders should consider Gamma along with Delta, Strike Price and time to expiry when assessing option risk.