The Greeks

The Greeks measure how an option's price changes in response to different factors. They're essential for understanding risk and managing positions.

First-Order Greeks

Greek	Measures	Question It Answers
Delta	Price sensitivity	How much does the option move if underlying moves $1?
Gamma	Delta sensitivity	How fast does delta change?
Theta	Time decay	How much value do I lose per day?
Vega	Volatility sensitivity	How much does price change if IV moves 1%?

Second-Order Greeks

Greek	Measures	Question It Answers
Vanna	Delta-vol sensitivity	How does delta change when IV moves?
Volga	Vega-vol sensitivity	How does vega change when IV moves?
Charm	Delta-time sensitivity	How does delta change as time passes?

Quick Reference

                    CALL                    PUT
Delta (Δ)          0 to +1                -1 to 0
Gamma (Γ)          Always positive        Always positive
Theta (Θ)          Usually negative       Usually negative
Vega (ν)           Always positive        Always positive

How They're Related

The Greeks are derived from the Black-Scholes model and are interconnected:

• Gamma is the rate of change of delta
• Theta and gamma are related - high gamma positions have high theta
• Vanna measures how delta changes with vol (∂Δ/∂σ)
• Volga measures how vega changes with vol (∂ν/∂σ)
• Charm measures how delta decays over time (∂Δ/∂t)
• ATM options have the highest gamma, theta, and vega

In Practice

If you're...	Watch...
Directional trading	Delta, Charm
Near expiry	Gamma, Theta
Trading volatility	Vega, Volga
Hedging dynamically	Delta, Gamma, Vanna
Managing skew exposure	Vanna

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Related:

• Black-Scholes Model - Where the Greeks come from
• Lesson 6: Greeks 101 - Full explainer with examples
• Lesson 8: Greeks Beyond the Basics - Advanced Greeks in depth