Option greeks
Greeks measure how an option's price changes as each variable moves: underlying, time, volatility and rates. They are the option trader's instrument panel — without them you fly blind. Every card includes a numeric example; then practice with the Black-Scholes calculator in the Options section.
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Delta (Δ) — direction
How much the premium changes if the underlying rises $1. A call with 0.50 delta gains ~$0.50 per $1 move; puts have negative delta. ATM ≈ ±0.50; deep ITM → ±1; far OTM → 0. Also read as the approximate probability of expiring ITM (0.30 delta ≈ 30%) and as share equivalence: one 0.50-delta call ≈ 50 shares (with the 100 multiplier).
Gamma (Γ) — acceleration
How much DELTA changes if the underlying rises $1. With delta 0.50 and gamma 0.08, after a $1 rally delta becomes 0.58. Highest for ATM options near expiry — which is why option prices move explosively in the final week. Option buyers are long gamma (acceleration works for you); sellers are short gamma (it works against you).
Theta (Θ) — the rent of time
How much the option loses per passing day, all else equal. Theta -0.05 = the premium bleeds $5/day per contract (100 multiplier). It is not linear: decay accelerates brutally in the last 30-45 days for ATM options. Buyers pay this 'rent' daily; sellers collect it. That is why buying short-dated OTM options and waiting is a money-losing machine.
Vega (V) — volatility sensitivity
How much the premium changes if implied volatility rises 1 percentage point. Vega 0.12 = +$12 per contract if IV goes from 30% to 31%. Critical around earnings: IV inflates before the report and collapses after (IV crush) — you can get the direction right and still lose because you bought expensive vega. Long options = positive vega; short = negative.
Rho (ρ) — interest rates
How much the premium changes if the risk-free rate rises 1 point. Rho 0.04 = +$4 per contract. The least-watched greek because its short-term effect is small, but it matters for LEAPS (options over a year out) and during aggressive hiking cycles: calls gain value with higher rates, puts lose.
Implied volatility (IV) and its rank
IV is the volatility the market 'quotes' inside the premium — the expectation of future movement, not the past. Always compare it against its own history using IV Rank/Percentile: 40% IV can be very expensive on an index and cheap on a biotech. Professional rule: high IV (rank >50) favours SELLING strategies (collect inflated premium); low IV favours BUYING options.