Understanding Option Greeks

Option Greeks are mathematical calculations that help traders understand how option prices change in response to various factors. They’re essential for risk management and strategy optimization.

The Five Main Greeks

Greek	Measures	Key Question
Delta (Δ)	Price sensitivity	How much will option price change if stock moves $1?
Gamma (Γ)	Delta sensitivity	How much will delta change if stock moves $1?
Theta (Θ)	Time decay	How much value lost per day?
Vega (ν)	Volatility sensitivity	How much will price change if IV changes 1%?
Rho (ρ)	Interest rate sensitivity	How much will price change if rates change 1%?

Delta (Δ) - Direction and Probability

What Delta Tells You

Delta measures how much an option’s price changes when the underlying stock moves $1.

Delta Ranges:

Call options: 0 to 1.0
Put options: -1.0 to 0
ATM options: ~0.5 (calls) or ~-0.5 (puts)

Delta as Probability

Delta approximates the probability of finishing in-the-money:

0.30 delta = ~30% chance of finishing ITM
0.70 delta = ~70% chance of finishing ITM

Delta Examples

Call Option Example:

Stock price: $100
Call delta: 0.60
If stock rises to $101: Option gains $0.60
If stock falls to $99: Option loses $0.60

Portfolio Delta:

Own 5 call contracts with 0.40 delta
Total delta: 5 × 100 × 0.40 = 200
Position behaves like owning 200 shares

Using Delta in Optionomics

Our platform shows:

Real-time delta for all options
Portfolio delta exposure
Delta-neutral hedging opportunities
Delta flow analysis

Gamma (Γ) - The Rate of Change

What Gamma Tells You

Gamma measures how fast delta changes as the stock price moves.

Gamma Characteristics:

Highest for ATM options
Increases near expiration
Same for calls and puts
Always positive for long options

Gamma Risk

High gamma means:

Delta changes rapidly
Position becomes directional quickly
More frequent hedging needed
Greater profit/loss potential

Gamma Example

Scenario:

ATM option with delta 0.50, gamma 0.05
Stock rises $1:
- New delta: 0.50 + 0.05 = 0.55
- Option gains: ~$0.525 (average delta)
Stock rises $2:
- New delta: 0.50 + (0.05 × 2) = 0.60
- Option gains: ~$1.10

Gamma Exposure (GEX)

Market makers’ gamma exposure affects market dynamics:

Positive GEX: Dealers sell rallies, buy dips (stabilizing)
Negative GEX: Dealers buy rallies, sell dips (destabilizing)
Zero Gamma: Flip point between regimes

Theta (Θ) - Time Decay

What Theta Tells You

Theta measures daily time value loss, assuming all else equal.

Theta Characteristics:

Always negative for long options
Accelerates near expiration
Highest for ATM options
Affected by weekends and holidays

Theta Decay Curve

Time Value
    |
100%|●
    | \
 75%|  \
    |   ●
 50%|    \
    |     ●
 25%|      \●
    |       \●
  0%|________●___
    30  20  10  0
    Days to Expiration

Theta Example

Option Details:

Premium: $3.00
Theta: -0.10
Days to expiration: 30

Time Decay:

Tomorrow: Worth $2.90
In 1 week: Worth ~$2.30
In 2 weeks: Worth ~$1.60 (accelerating)

Weekend Theta

Markets price in weekend decay:

Friday’s theta includes weekend
Monday opens with less time value
Important for weekly options

Vega (ν) - Volatility Sensitivity

What Vega Tells You

Vega measures option price change per 1% change in implied volatility.

Vega Characteristics:

Highest for ATM options
Higher for longer expirations
Same for calls and puts
Positive for long options

Vega Example

Scenario:

Option price: $5.00
Vega: 0.20
Current IV: 30%

If IV rises to 31%:

New price: $5.00 + $0.20 = $5.20

If IV falls to 25%:

New price: $5.00 - (5 × $0.20) = $4.00

Volatility Events

Vega crucial around:

Earnings announcements
Economic data releases
Federal Reserve meetings
Major news events

Rho (ρ) - Interest Rate Sensitivity

What Rho Tells You

Rho measures option price change per 1% change in interest rates.

Rho Characteristics:

Usually smallest Greek impact
More significant for LEAPS
Positive for calls, negative for puts
Affected by dividend yields

When Rho Matters

Long-dated options (>6 months)
High interest rate environments
Deep ITM options
Dividend-paying stocks

Greeks Relationships

Delta-Gamma Relationship

Gamma is the rate of delta change
High gamma = unstable delta
Low gamma = stable delta

Theta-Vega Trade-off

Selling options: Collect theta, short vega
Buying options: Pay theta, long vega
Calendar spreads: Theta positive, vega positive

Greeks Over Time

Greek	Near Expiration	Far from Expiration
Delta	Approaches 0 or 1	More stable
Gamma	Very high ATM	Lower, distributed
Theta	Accelerates	Slower decay
Vega	Decreases	Higher
Rho	Minimal	More significant

Using Greeks for Risk Management

Position Greeks

Calculate portfolio Greeks:

Example Portfolio:

Long 10 AAPL 150 Calls (Δ=0.6, Γ=0.02, Θ=-0.15, ν=0.25)
Short 5 AAPL 160 Calls (Δ=0.3, Γ=0.03, Θ=-0.10, ν=0.20)

Net Greeks:

Delta: (10×0.6) - (5×0.3) = 4.5 (450 share equivalent)
Gamma: (10×0.02) - (5×0.03) = 0.05
Theta: (10×-0.15) - (5×-0.10) = -1.0 ($100/day decay)
Vega: (10×0.25) - (5×0.20) = 1.5

Greek Neutral Strategies

Delta Neutral:

No directional bias
Profit from volatility or time decay
Examples: Straddles, iron condors

Gamma Neutral:

Stable delta hedging
Reduced rebalancing needs
Examples: Ratio spreads

Vega Neutral:

Immune to IV changes
Focus on directional moves
Examples: Vertical spreads

Greeks in Optionomics Platform

Real-Time Greeks Display

Live Greeks for all options
Portfolio Greeks summary
Greeks charts and visualizations
Historical Greeks data

Greeks-Based Analytics

Gamma exposure (GEX) levels
Delta exposure analysis
Vega-weighted IV
Theta burn rates

AI Greeks Analysis

Optimal Greek exposures
Risk alerts based on Greeks
Greeks-based trade suggestions
Risk management strategies

Practical Greeks Examples

Example 1: Earnings Play

Strategy: Long straddle before earnings

High vega (profit from IV expansion)
Delta neutral (no directional bias)
Negative theta (time decay cost)

Example 2: Income Generation

Strategy: Short iron condor

Positive theta (collect decay)
Short vega (want IV to fall)
Gamma negative (risk if moves)

Example 3: Directional Bet

Strategy: Long call spread

Positive delta (bullish)
Reduced vega (less IV risk)
Limited gamma (capped risk)

Common Greeks Mistakes

Ignoring Gamma Risk: Not understanding acceleration
Underestimating Theta: Holding too long
Vega Surprises: IV crush after events
Delta Assumptions: Using as exact hedge ratio
Rho Neglect: Important for LEAPS

Greeks Cheat Sheet

Situation	Important Greeks	Strategy Consideration
Day Trading	Delta, Gamma	High gamma for leverage
Earnings	Vega, Theta	Vega long or short?
Income	Theta, Delta	Positive theta focus
Hedging	Delta, Gamma	Match portfolio Greeks
Long-term	Rho, Vega	Consider rate impact

Advanced Greeks Concepts

Second-Order Greeks

Vanna: Delta change from volatility
Charm: Delta decay over time
Vomma: Vega change from volatility
Speed: Gamma change from price

Cross-Greeks Effects

Volatility affects delta (vanna)
Time affects delta (charm)
Price affects vega (vanna)

Key Takeaways

Delta: Direction and hedge ratio
Gamma: Rate of change and risk
Theta: Time decay cost/benefit
Vega: Volatility exposure
Rho: Interest rate sensitivity
Together: Complete risk picture

Next Steps

Continue learning:

Pro Tip: Use Optionomics’ Greeks analysis to understand market maker positioning and identify optimal entry/exit points based on Greek exposures.

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Understanding Option Greeks