Options Greeks

Options greeks quantify how an option’s price reacts to market changes. Use options greeks to track direction, convexity, time decay, volatility, and rates. They help you size trades, hedge, and set expectations.

What is options greeks?

• Delta (Δ): price change per $1 move in the underlying. Calls ≈ +0 to +1. Puts ≈ 0 to -1.
• Gamma (Γ): change in delta per $1 move. Higher near-the-money, shorter dated.
• Theta (Θ): time decay per day. Usually negative for long options.
• Vega (ν): price change for a 1 point change in implied volatility (IV).
• Rho (ρ): price change for a 1% (100 bps) interest rate change.
• Net greeks: sum per position or strategy (e.g., spreads, iron condors).

Why it matters for options traders

• Measure directional exposure (Delta).
• See how fast delta can change (Gamma).
• Plan decay impact over days (Theta).
• Anticipate IV shifts around events (Vega).
• Understand rate sensitivity for long-dated options (Rho).
• Compare strategies on risk, not just payoff diagrams.
• Set hedges and position sizes with clearer expectations.

Step-by-step with concrete numbers

Assume:

• Underlying: $100
• Long 30-day $100 call price: $3.50
• Greeks now: Δ = +0.40, Γ = 0.05, Θ = -0.07/day, Vega = 0.10 per IV point, Rho = +0.02 per 1% rate

Price move only (today):

• Underlying +$1 to $101
  • Estimated option change ≈ +0.40 → $3.90
  • New delta ≈ 0.40 + (0.05 × $1) = 0.45
• Another +$1 to $102 (using updated delta 0.45)
  • Change ≈ +0.45 → $4.35
  • New delta ≈ 0.50
• Insight: Gamma accelerates gains (and losses) as price moves.

Time passes, no move, no IV change:

• 1 day later
  • Theta drag ≈ -$0.07 → $3.43

Volatility change only (today):

• IV up 2 points (e.g., 25% → 27%)
  • Vega impact ≈ 0.10 × 2 = +$0.20 → $3.70
• IV down 1 point
  • ≈ -$0.10 → $3.40

Rates change only:

• Rates +1%
  • Rho ≈ +$0.02 → $3.52

Combine effects (today):

• Underlying +$1 and IV -1 point
  • Delta: +$0.40
  • Vega: -$0.10
  • Net ≈ +$0.30 → $3.80 Note: Greeks are approximations at a moment in time. They update as price, IV, and time change.

Common mistakes & risk

• Ignoring theta on long premium. Time decay compounds daily.
• Treating greeks as fixed. Gamma and vega shift quickly near-the-money.
• Mixing units. Vega is per IV point, not percent of price.
• Over-hedging delta without rebalancing for gamma.
• Forgetting event risk. IV can crush after earnings.
• Assuming model certainty. Greeks come from models and inputs; liquidity and slippage matter.

Analyze with ImpliedOptions

• Build multi-leg strategies and view net greeks:
  • Strategy Builder: /strategy-builder
• Simulate price, time, and IV scenarios. See P/L alongside greeks:
  • Profit Calculator: /analysis
• Compare alternatives. Align delta, theta, and vega with your plan before entering.

FAQ

• What greek should I watch first?
  • Start with Delta for direction and Theta for decay. Add Vega if IV is likely to move.
• Why is put delta negative?
  • Put prices rise when the underlying falls. The negative delta reflects that inverse move.
• How often do greeks change?
  • Constantly. Price ticks, IV shifts, and time passing all update greeks in real time.
• Is higher gamma always better?
  • It cuts both ways. High gamma helps when price moves in your favor and hurts when it moves against you.
• Do long options always lose to theta?
  • Theta is a headwind, but moves in price or IV can offset it. Timing and sizing are key.