Option Greeks

Option greeks quantify how an option’s price reacts to market forces. Use option greeks to estimate moves from price, time, volatility, and rates. They help you pick structures, size risk, and hedge. Core greeks:

• Delta: price sensitivity
• Gamma: delta’s rate of change
• Theta: time decay
• Vega: implied volatility sensitivity
• Rho: interest rate sensitivity

What is option greeks?

• Delta (−1 to +1): Option price change for a $1 move in the underlying.
• Gamma (>0 for long options): How much delta changes per $1 move.
• Theta (usually negative for longs): Daily time decay.
• Vega (positive for long options): Option price change for a 1 percentage-point IV move.
• Rho: Option price change for a 1 percentage-point interest-rate move.
• Note: Greeks are per share. One contract typically controls 100 shares.

Why it matters for options traders

• Forecast P/L drivers: price, time, and volatility.
• Compare strategies: choose structures with target delta/theta/vega.
• Manage risk: cap exposure and hedge directional bias.
• Time events: plan for IV crush or expansion.
• Adjust positions: respond as greeks evolve with price and time.

Step-by-step with concrete numbers

Setup:

• Underlying: $500
• 30 DTE, 500 call priced at $8.00 ($800 per contract)
• Greeks (per share): Delta +0.52, Gamma 0.07, Theta −0.12/day, Vega +0.10 per +1% IV, Rho small

Scenarios (approximate):

• Price up $2 today:
  • Change ≈ Delta×$2 + 0.5×Gamma×$2^2
  • = 0.52×2 + 0.5×0.07×4 = 1.04 + 0.14 = +$1.18
  • New premium ≈ $9.18 ($918 per contract)
• Price flat; IV +2 pts:
  • Vega impact = 0.10×2 = +$0.20 → $8.20 ($820/contract)
• One day passes; flat; IV unchanged:
  • Theta impact = −$0.12 → $7.88 ($788/contract)
• Combine: up $2; IV +2; one day passes:
  • $8.00 + 1.18 + 0.20 − 0.12 ≈ $9.26 ($926/contract)

Notes:

• Short options flip signs: theta helps, vega hurts, gamma risk increases.
• Gamma is larger near expiration. Delta can change fast intraday.
• Rho matters more for long-dated options.

Common mistakes & risk

• Ignoring theta: holding long options into fast decay.
• Misreading delta as exact probability. It is only a rough proxy.
• Underestimating gamma near expiration. Small price moves can swing P/L.
• Chasing high IV without a vega plan. IV crush can overwhelm direction.
• Mixing units. Remember greeks are per share; multiply by 100 per contract.
• Not stress-testing. Consider combined moves in price, IV, and time.

Analyze with ImpliedOptions

• Build by greeks:
  • Use the Strategy Builder to target delta, theta, and vega that fit your outlook.
• Simulate scenarios:
  • Use the Profit Calculator to map P/L for price, days, and IV changes.
• Iterate:
  • Check position greeks before and after adjustments.
  • Compare alternatives (e.g., debit vs credit spreads) by net greeks.

FAQ

• What are the main option greeks?

  • Delta, gamma, theta, vega, and rho.

• Which greek matters most for short-term trades?

  • Gamma and theta. Delta moves quickly; decay is fastest near expiry.

• How do I reduce delta risk?

  • Use spreads, add offsetting options, or hedge with shares.

• Why did my option fall after earnings despite a price rise?

  • IV crush. Vega turned negative P/L even with favorable direction.

• Do greeks stay constant?

  • No. They change with price, time, IV, and proximity to strike.