Gamma

Gamma measures how fast your delta changes as the stock moves, making it the “acceleration” of option pricing. Think of it like driving a car – if delta is your speed, gamma is how quickly you can speed up or slow down. For option buyers, gamma is the secret weapon that creates those massive overnight gains when a stock makes a big move. For option sellers, gamma is the hidden risk that can turn a profitable position into a significant loss faster than you might expect. Understanding gamma is crucial for managing risk and knowing when positions can rapidly move against you.

How Gamma Works

Gamma is expressed as the change in delta per $1 stock move:

  • A gamma of 0.05 means delta changes by 0.05 for each $1 move
  • Always positive for long positions (helps you)
  • Always negative for short positions (hurts you)

Gamma in Action

Long $50 call with 0.50 delta and 0.10 gamma:

  • Stock rises to $51: Delta becomes 0.60 (0.50 + 0.10)
  • Stock rises to $52: Delta becomes 0.70 (0.60 + 0.10)
  • Gains accelerate as stock continues higher

Short $50 put with -0.50 delta and -0.10 gamma:

  • Stock falls to $49: Delta becomes -0.60
  • Stock falls to $48: Delta becomes -0.70
  • Losses accelerate as stock continues lower

Gamma by Strike and Time

Gamma varies predictably:

ATM Options: Maximum gamma

  • Delta changes most rapidly
  • Highest risk/reward
  • Most sensitive to stock moves

ITM/OTM Options: Lower gamma

  • Delta changes slowly
  • More predictable behavior
  • Less explosive moves

Near Expiration: Gamma explodes

  • ATM gamma can exceed 0.50
  • Small moves create huge swings
  • “Gamma risk” at its highest

Time Effect Example

$50 ATM call gamma:

  • 45 DTE: 0.02 gamma
  • 21 DTE: 0.04 gamma
  • 7 DTE: 0.08 gamma
  • 1 DTE: 0.25+ gamma

The closer to expiration, the more explosive gamma becomes.

The Gamma Profit Engine

For buyers, gamma creates non-linear profits:

Big Move Example

Buy $50 call for $1.00, stock at $50:

  • Initial: 0.50 delta, 0.10 gamma
  • Stock to $52: Delta now 0.70, option worth ~$2.40
  • Stock to $54: Delta now 0.90, option worth ~$4.20
  • Profit: 320% from 8% stock move

Without gamma acceleration, profit would be linear and much smaller.

The Gamma Risk Trap

For sellers, gamma creates accelerating losses:

Risk Example

Sell $50 put for $0.50, stock at $52:

  • Initial: -0.25 delta, -0.05 gamma
  • Stock to $50: Delta now -0.50, loss $0.50
  • Stock to $48: Delta now -0.75, loss $2.00
  • Loss: 4x the premium collected

This acceleration is why risk management is critical for sellers.

Gamma Scalping

Advanced traders profit from gamma without direction:

  1. Buy ATM straddle (long call + put)
  2. High positive gamma position
  3. Stock moves up: Sell shares (delta hedge)
  4. Stock moves down: Buy shares (delta hedge)
  5. Profit from oscillation

Requires active management but profits from volatility.

Managing Gamma Risk

For Sellers:

  • Avoid ATM strikes near expiration
  • Sell 15-30 delta for lower gamma
  • Close or roll before final week
  • Size positions for worst-case gamma

For Buyers:

  • Target ATM for maximum gamma
  • Buy before expected movement
  • Take profits on gamma expansion
  • Don’t overpay for gamma

Gamma and Weekly Options

Weekly options have compressed gamma effects:

Weekly Gamma Timeline

  • Monday: Moderate gamma
  • Wednesday: Gamma increasing
  • Thursday: High gamma risk
  • Friday: Extreme gamma

This is why many weekly sellers close by Wednesday/Thursday.

The Gamma/Theta Relationship

High gamma always comes with high theta:

  • ATM options: Max gamma, max theta
  • Sellers must balance income vs risk
  • Buyers pay heavy time decay for gamma

Strategy Implications

Selling sweet spot: 20-30 delta

  • Reasonable theta income
  • Manageable gamma risk
  • Better risk/reward

Buying sweet spot: 40-60 delta

  • Good gamma exposure
  • Tolerable theta decay
  • Balanced approach

Gamma in Popular Strategies

Short Strangles/Iron Condors:

  • Negative gamma on both sides
  • Risk if stock moves sharply
  • Profit targets critical

Calendar Spreads:

  • Long gamma far out
  • Short gamma near term
  • Profits from gamma differential

Butterfly Spreads:

Real-World Gamma Events

Earnings announcements create gamma explosions:

Earnings Example

Stock at $100, ATM straddle before earnings:

  • Combined gamma: 0.20
  • Stock gaps to $110: Calls gain $8+
  • Stock gaps to $90: Puts gain $8+
  • Straddle cost $4, potential profit 100%+

This gamma expansion explains earnings lottery appeal.

Gamma Risk Management Rules

Position Sizing:

  • Never sell more gamma than you can handle
  • Consider 10% move scenario
  • Size for assignment acceptance

Time Management:

  • Reduce gamma exposure near expiration
  • Roll or close high gamma positions
  • Avoid gamma storms (final days)

Strike Selection:

  • Understand gamma profile
  • Balance premium vs risk
  • Prefer lower gamma for income

Common Gamma Mistakes

Sellers: Holding through expiration week Buyers: Overpaying for gamma pre-event Both: Ignoring gamma’s exponential nature Portfolio: Too much gamma concentration

Building Gamma Awareness

Track your portfolio gamma:

  • Sum all position gammas
  • Monitor changes daily
  • Adjust when excessive
  • Balance long/short gamma

Portfolio Example

  • Short 10 puts: -0.50 gamma
  • Long 5 calls: +0.25 gamma
  • Net: -0.25 gamma (bearish acceleration)

This helps anticipate portfolio behavior.

Key Takeaways

Gamma:

  • Measures delta’s rate of change
  • Creates non-linear profits/losses
  • Highest for ATM options
  • Explodes near expiration
  • Positive for buyers, negative for sellers
  • The source of option leverage

Gamma is why options offer asymmetric returns – small moves can create large profits for buyers or large losses for sellers. Respect gamma, especially in the final week of an option’s life, and size positions accordingly. For income traders, managing gamma risk is just as important as collecting theta.