The Greeks simply explained: delta, gamma, theta and vega

What you will learn

• What delta, gamma, theta and vega measure and their usual ranges
• How to estimate an option's price change from several Greeks at once
• How to calculate position delta in share equivalents
• Where the Greek estimates stop being reliable

Explanation

The Greeks are sensitivity measures. Each one tells you how much the option price changes when one input changes and all others stay the same. They come from an option pricing model and are shown in most broker platforms. Values here are per share; multiply by the multiplier and the number of contracts for the position.

Delta

Delta (Δ) is the change in the option price for a €1 change in the underlying. Calls have a delta between 0 and +1, puts between −1 and 0. At-the-money options have a delta near ±0.50; deep in-the-money options approach ±1; far out-of-the-money options approach 0.

Two practical uses:

• Share equivalents: position delta = delta × multiplier × contracts. A position delta of +150 behaves for small moves like holding 150 shares.
• Hedge ratio: to neutralise a position delta of +150, you could sell 150 shares. This is called delta hedging.

Delta is sometimes used as a rough indication of the probability that the option expires in the money. This is only an approximation from the model, not a real probability.

Gamma

Gamma (Γ) is the change in delta for a €1 change in the underlying. It is highest for at-the-money options close to expiry. Long options have positive gamma: the position becomes more long as the price rises and more short as it falls, which helps the holder. Short options have negative gamma: moves work increasingly against the seller.

Theta

Theta (Θ) is the change in the option price for one day passing, all else equal. For long options it is usually negative: this is time decay. Decay is not linear. For at-the-money options it speeds up in the last weeks before expiry. Short option positions have positive theta.

Vega

Vega is the change in the option price for a 1 percentage point change in implied volatility (for example from 25% to 26%). Long options have positive vega. Vega is larger for options with more time to expiry. (A fifth Greek, rho, measures sensitivity to interest rates; it is usually small for short-dated options.)

Combining the Greeks

A useful approximation for the change in option price:

Change ≈ Δ × ΔS + ½ × Γ × (ΔS)² + Θ × days + vega × ΔIV

ΔS is the change in the underlying in euros, ΔIV the change in implied volatility in percentage points.

Worked example

Hypothetical example: you hold 3 call contracts, multiplier 100. Share price €100, option price €5.00. Greeks per share: delta 0.50, gamma 0.04, theta −0.05 per day, vega 0.20. No fees.

Position delta: 0.50 × 100 × 3 = 150 share equivalents. A €1 rise in the share adds about €150.

Scenario 1: the share rises €2 in one day, IV unchanged.

• Delta: 0.50 × 2 = €1.00
• Gamma: ½ × 0.04 × 2² = 0.5 × 0.04 × 4 = €0.08
• Theta: −0.05 × 1 = −€0.05
• Total ≈ €1.00 + €0.08 − €0.05 = €1.03. New price ≈ €6.03. Position: €1.03 × 300 = +€309.
• New delta ≈ 0.50 + 0.04 × 2 = 0.58, so the position now behaves like 174 shares.

Scenario 2: the share is unchanged after one day, but IV falls 5 percentage points.

• Theta: −€0.05; vega: 0.20 × (−5) = −€1.00
• Total ≈ −€1.05. New price ≈ €3.95. Position: −€1.05 × 300 = −€315.

The share did not move, yet the position lost more than 20%. Vega and theta matter as much as direction.

Common mistake

Practice activity

Hypothetical: you hold 2 put contracts, multiplier 100. Put price €3.00. Greeks per share: delta −0.40, gamma 0.05, theta −0.04 per day, vega 0.15. Over 2 days the share falls €3 and IV rises 2 percentage points.

1. Calculate the position delta before the move.
2. Estimate the change in the put price per share, using all four Greeks.
3. Estimate the new put price and the change in value of the position.

Key takeaways

• Delta measures price sensitivity and gives share equivalents; gamma measures how fast delta changes.
• Theta is time decay, usually negative for buyers and accelerating near expiry for at-the-money options.
• Vega shows how much a 1-point change in implied volatility moves the price.
• Greek estimates work for small moves; re-price for large moves.

Next step

In the next lesson you will combine options and shares into basic strategies: the covered call, the protective put and vertical spreads.