Options Greeks Cheat Sheet

By the FinLingo Team | Capital markets practitioner, front office experience at a major European investment bank. FinLingo covers 342 lessons from bonds to exotic derivatives. About · Last updated: April 17, 2026

The Greeks are the five risk numbers every options trader watches. Each one measures how the option price responds to a different market input. This cheat sheet reduces each Greek to its essential intuition — what it is, when it matters, and what to watch for on the desk.

The Five Greeks in One Line Each

Delta: how much the option price moves when the underlying moves €1. Sits in [0, 1] for calls and [-1, 0] for puts. Deep ITM options have delta close to ±1; deep OTM options have delta close to 0. At the money, delta sits near ±0.5.

Gamma: how much Delta changes when the underlying moves €1. Gamma peaks at the money and decays into the wings. High gamma means your hedge becomes wrong quickly — the dynamic hedging cost is priced in gamma.

Vega: how much the option price changes when implied volatility moves 1%. Long options are long vega. At-the-money long-dated options carry the most vega. Vega is the dominant Greek for traders running volatility books.

Theta: time decay per calendar day. Short-dated ATM options lose value fastest. Theta is the rent you pay for holding optionality — the reason short-option strategies exist.

Rho: how much the option price moves when the risk-free rate moves 1 basis point. Small for short-dated equity options. Matters for long-dated fixed-income derivatives and for rate-sensitive exotic payoffs.

When Each Greek Matters

On a single vanilla position, all five Greeks are in play but not equally. For a short-dated equity option, Delta and Gamma dominate the daily P&L, Theta is the background drag, Vega moves on vol shocks, and Rho is essentially ignored.

For a long-dated swaption or a structured product with embedded duration, the ranking flips: Rho becomes a headline risk, Vega follows, Gamma and Theta become secondary, and Delta is often hedged out by design.

Portfolio-level Greeks aggregate linearly across positions. A trader’s book can be delta-neutral and still carry significant gamma or vega — the risk system reports each Greek separately for exactly this reason.

Practical Formulas from Black-Scholes

Under Black-Scholes, the Greeks have clean closed forms. Let d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T) and d₂ = d₁ − σ√T. Then for a European call: Delta = N(d₁). For the put: Delta = N(d₁) − 1. Gamma (same for call and put) = φ(d₁) / (Sσ√T). Vega (per 1% vol move) = Sφ(d₁)√T / 100. These four formulas cover 90% of desk usage.

The moneyness of an option — whether S is above, at, or below K — drives where each Greek sits in its natural range. ATM options have the highest gamma and vega per unit of price. Deep ITM or OTM options concentrate in delta (near ±1 or 0) and lose gamma and vega rapidly.

Reading a Risk Sheet

Bank risk systems display Greeks per position and aggregated per book. Typical risk-sheet conventions: Delta quoted in shares or notional (not the raw number between 0 and 1), Gamma quoted per 1% move in the underlying, Vega quoted per 1% vol move, Theta quoted in daily € P&L, Rho quoted per basis point. These scalings exist to make numbers comparable across books and products.

When you see a book’s Greeks listed, read them in the order of their P&L dominance for that book’s typical time horizon. A delta-hedged market-maker reads gamma and vega first. A long-dated fixed-income desk reads rho and vega first.