Gamma

Gamma is considered the second-order derivative in options trading, following Delta, which is the first-order derivative. While Delta measures how much the price of an option changes with a one-point move in the underlying asset, Gamma measures how much the Delta itself changes when the underlying asset price changes. Think of Delta as the speed of change, and Gamma as the acceleration.

In our Delta discussion, we highlighted that Delta works well for small price movements. But when the price changes significantly, Gamma becomes essential. This is because Delta isn't linear, it shifts based on the price action of the underlying.

Example:

Let’s say a Nifty 17,700 Call option (August 2022 expiry) is trading at ₹195 with a Delta of 0.55 and a Gamma of 0.0008.

• If Nifty rises by 100 points to 17,800, the option will gain ₹55.08 (100 × (0.55 + 0.0008)). The new premium becomes ₹250.08, and the updated Delta is 0.5508.
• If Nifty drops by 100 points to 17,600, the option would fall by ₹54.92 (100 × (0.55 - 0.0008)). The premium now becomes ₹140.08, with a Delta of 0.5492.

Gamma is crucial for traders using Delta hedging strategies, as it indicates how rapidly Delta will shift with market moves. It's equally important for traders who want to gauge how their P&L might fluctuate due to changes in Delta.

Long Gamma: Targeting In-The-Money Profits

Gamma is always positive for long options positions. A Long Gamma means the position benefits from the underlying price moving in either direction, due to acceleration in Delta.

• Long Call (Positive Gamma):
  When the underlying price increases, Gamma adds to the Delta, pushing it toward +1 and making the option more in-the-money. When the price falls, Gamma subtracts from Delta, pushing it closer to zero.
• Long Put (Positive Gamma):
  Since long puts have negative Delta, a price drop increases the Delta's negativity (moving toward -1), making it more in-the-money. Conversely, if the price rises, Gamma reduces the negativity of Delta, making it less in-the-money.

In essence, Long Gamma = faster profit or loss acceleration based on market movement.

Short Gamma: Aiming to Stay Out-of-the-Money

A Short Gamma position has negative Gamma exposure. This means that as the underlying price moves, Delta shifts in a way that generally works against the position.

• Short Call (Negative Gamma):
  If the underlying price drops, Gamma adds to the Delta, making it less negative and shifting it toward zero. If the price rises, Gamma subtracts from Delta, making it more negative and pushing the option deeper in-the-money.
• Short Put (Negative Gamma):
  If the price increases, Gamma reduces the Delta, making it less positive. But if the price decreases, Gamma adds to Delta, increasing the in-the-money risk.

Short Gamma positions are inherently riskier, especially in volatile markets, as they are more sensitive to rapid price moves.

Moneyness and Gamma

Gamma is highest when an option is at-the-money (ATM) and declines symmetrically as it moves either in-the-money (ITM) or out-of-the-money (OTM). The Gamma profile forms a bell curve centred around the ATM strike.

• ATM options have the greatest Gamma impact because Delta is around 0.50, and even minor price changes cause significant Delta adjustments.
• Deep ITM options (Delta near +1 for calls, -1 for puts) and far OTM options (Delta near 0) exhibit minimal Gamma movement.

Gamma Near Expiry

As the expiry date approaches:

• ATM Gamma spikes: The Gamma curve becomes sharper and more pronounced.
• ITM and OTM Gamma falls: These options become less reactive to price changes.

This means ATM options close to expiration are highly sensitive and can swing sharply with even small moves in the underlying.

Impact of Volatility on Gamma

Volatility changes impact Gamma differently across moneyness levels:

• Rising Volatility:
  Increases Gamma for ITM and OTM options but reduces Gamma for ATM options.
• Falling Volatility:
  Increases ATM Gamma while reducing Gamma for ITM and OTM options.

Understanding this dynamic is crucial for traders building strategies around volatility expectations.

Conclusion

Gamma might seem secondary to Delta in simple option trades like outright buying or selling. However, in multi-leg or complex strategies, Gamma becomes vital.

For instance:

• A position with positive Delta and positive Gamma benefits strongly from an upward price move.
• But a positive Delta and negative Gamma scenario means the Delta will erode as the price rises, eventually leading to losses unless carefully managed.

Traders must track Gamma exposure to determine when to book profits or cut losses effectively.

Point to Remember

• Gamma has limited application in plain vanilla option trades but is indispensable in complex strategies.
• All long options carry positive Gamma.
• A position with both positive Delta and Gamma benefits from rising prices.
• A positive Delta with negative Gamma setup risks turning unprofitable if not actively managed.