Greeks without a single formula

The Greeks are sensitivities. Each one tells you how the option price changes when one specific input (spot, vol, time, rates) moves. Forget the partial derivatives — they're just the formal way to write "how much does the price move when X moves".

Delta (Δ) — your exposure to the underlying

Delta is how many units of the underlying you behave like. A call with Δ = 0.5 moves €0.50 when the spot moves €1. So 1 call = 0.5 share of stock, as far as your P&L is concerned.

• Deep ITM call: Δ near 1 (almost like holding the stock).
• ATM call: Δ ≈ 0.5.
• Deep OTM call: Δ near 0 (almost no exposure).
• Puts have negative delta (between 0 and −1).

Why traders care: to hedge a long-call position, you short Δ shares of stock. Then you're flat on direction — your P&L only depends on how the other Greeks move.

Gamma (Γ) — how exposure changes

Delta isn't constant. It changes as spot moves. Gamma measures how fastdelta changes. Long gamma = your exposure increases when the market moves with you and decreases when it moves against. That's a good position to be in.

• Long any option (call or put) → long gamma. Both buyers benefit from large moves in either direction.
• Short any option → short gamma. You're hurt by large moves.
• ATM near maturity → highest gamma. Tiny spot moves swing the delta enormously, which is why pinning effects exist near expiry.

Vega — sensitivity to uncertainty

Vega is how much the option price changes when implied vol moves by 1 vol-point. A call with vega = 0.30 gains €0.30 if IV moves from 20% to 21%. Long any option = long vega. Short any option = short vega.

Vega is biggest for ATM options at long maturities. It shrinks both as you move ITM/OTM and as you approach expiry — because the option becomes either almost-deterministic (close to its intrinsic value) or worth almost nothing.

Theta (Θ) — the daily rent

Every day that passes, an option loses a bit of its time value. Theta is that daily decay. A call with theta = −€0.05 loses 5 cents each day, all else equal. The seller pockets it; the buyer pays it.

Theta is a counterweight to gamma. If you're long an option, you're long gamma (good when markets move) but short theta (paying daily rent). Short an option: opposite. Whether you make money depends on whether the realized moves cover the rent — that's the entire vol-trading game.

The four-letter mantra

Every option position has these four quantities. They're what you trade. When a structurer says "I want to sell vega and stay flat on delta", they mean they want to be exposed to a fall in vol but not to spot moves. That's a short straddle delta-hedged with the stock.

Once you can think in these four words, every options strategy becomes a recipe: combine instruments to dial up the Greeks you want and dial down the ones you don't.