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OPTIONS GREEKS

Core Concept: Greeks measure how options prices change with different variables (price, time, volatility).

Why It Matters​

Greeks predict P&L and risk. Without understanding them, you're trading blind.

When to Use​

✅ Use Greeks to:

  • Estimate profit/loss scenarios
  • Compare strategies
  • Hedge positions
  • Time entries/exits

❌ Don't:

  • Ignore them in multi-leg trades
  • Trade without checking theta decay
  • Forget they change as price moves

The Five Greeks​

Delta (Δ): Price sensitivity

  • Measures: How much option price changes per $1 stock move
  • Range: 0 to 1 (calls), 0 to -1 (puts)
  • ATM options ≈ 0.5 delta

Gamma (Γ): Delta sensitivity

  • Measures: How much delta changes per $1 stock move
  • Highest at ATM, accelerates near expiration
  • Risk metric for short options

Theta (Θ): Time decay

  • Measures: Daily option value loss from time passing
  • Always negative for long options
  • Accelerates in final 30-45 days

Vega (ν): Volatility sensitivity

  • Measures: Price change per 1% implied volatility move
  • Highest for ATM options
  • Long options benefit from rising IV

Rho (ρ): Interest rate sensitivity

  • Measures: Price change per 1% interest rate change
  • Usually negligible for short-term options

Trade-offs​

Pros: Quantifies risk, enables comparison, predicts scenarios
Cons: Changes constantly (requires monitoring), approximations not guarantees

Greeks connect to options_basics for understanding how premium is built and implied_volatility for vega impact.

Quick Reference​

GreekLong CallLong PutWhat It Means
Delta+0.5 (ATM)-0.5 (ATM)50% chance of being ITM
Gamma++Delta accelerates as stock moves
Theta--Lose value daily (~$10-50/day)
Vega++Benefit from volatility spike

Delta as probability: 0.30 delta ≈ 30% chance of expiring ITM

Portfolio Greeks: Sum individual position Greeks for net exposure

Key relationships:

High gamma = Unstable delta (good for long, risky for short)
High theta = Fast decay (bad for long, good for short)
High vega = IV sensitive (volatile premium swings)

Examples​

EXAMPLE

Delta scenario:

Stock: $100
ATM Call (100 strike): Delta = 0.50

Stock moves to $101 (+$1):

  • Option gains ~$0.50 (50% of stock move)

Stock moves to $105 (+$5):

  • Option gains ~$2.50 initially
  • But delta increases (gamma effect), actual gain might be $3.00

Theta decay acceleration:

45 DTE (Days to Expiration):

  • Option worth $5.00, theta = -0.05 ($5/day loss)

15 DTE:

  • Option worth $2.00, theta = -0.10 ($10/day loss)
  • Decay accelerates as expiration nears

Gamma risk on short options:

Sell OTM call at 0.20 delta ($105 strike, stock at $100)
Collect $200 premium

Stock gaps to $108:

  • Delta was 0.20, now 0.75 (gamma increased delta)
  • Loss: ~$300 (more than premium collected)
  • Gamma hurt because delta accelerated against you

Vega in earnings:

Before earnings:

  • 100 strike call: $3.00, IV = 50%, vega = 0.15

After earnings (no stock move, IV drops to 30%):

  • IV drops 20 points × 0.15 vega = $3.00 loss
  • Option now worth $0.00 (vega crush) ```

References​