An option's price is sensitive to multiple variables simultaneously. If you hold an options position, you need to know not just what it's worth today, but how it will change if the stock moves, if a week passes, or if market volatility shifts. The Greeks quantify each of these sensitivities precisely.
Delta (Δ) — sensitivity to stock price
Delta measures how much the option price changes for a £1 move in the underlying stock. A call with Delta 0.5 rises 50p if the stock rises £1. Delta ranges from 0 to 1 for calls and -1 to 0 for puts.
- At-the-money options: Delta ≈ 0.5 (calls) or -0.5 (puts)
- Deep in-the-money: Delta approaches 1 (call) — behaves like owning the stock
- Deep out-of-the-money: Delta approaches 0 — tiny sensitivity to price
Delta is also used as a probability proxy: a call with Delta 0.30 has roughly a 30% chance of expiring in the money.
Gamma (Γ) — the rate of change of Delta
Gamma measures how fast Delta itself changes. High Gamma means your hedge ratio changes rapidly — you need to rebalance more frequently. Options near expiry and near the money have the highest Gamma. For option sellers, high Gamma is dangerous: a sudden price move can dramatically shift your Delta exposure before you can react.
Theta (Θ) — time decay
Theta is the daily erosion of an option's value as it approaches expiry. An option loses value each day because there's less time for the underlying to make a favourable move.
Theta accelerates as expiry approaches — the time value decay curve is not linear but exponential in the final weeks. This is why option sellers love short-dated options (they collect Theta quickly) while option buyers prefer longer-dated ones.
Vega (V) — sensitivity to volatility
Vega measures how much the option price changes for a 1% change in implied volatility. Options become more valuable when volatility is high (more chance of a big move). Vega is always positive for both calls and puts — higher volatility helps all option buyers.
Rho (ρ) — sensitivity to interest rates
Rho measures sensitivity to interest rate changes. Generally the least important Greek for equity options but matters for long-dated options and rate-linked instruments.
How traders use the Greeks
Professional options desks manage portfolios by monitoring their aggregate Greek exposures — their total Delta, Gamma, Theta, and Vega across all positions. A "delta-neutral" portfolio has net Delta near zero — it doesn't make or lose money from small stock moves. A "Vega-neutral" portfolio doesn't change much if volatility shifts. Managing these exposures is the core of options market-making.
What this means for you
If you ever buy or sell options, Delta and Theta are the two Greeks to understand first. Delta tells you how much you make per unit move in the underlying; Theta tells you how much you're paying each day for the right to hold the option. The tradeoff between the two is the fundamental tension of options trading: time works against buyers and for sellers, while big moves work for buyers and against sellers.