The Greeks — Delta, Gamma, Theta & Vega

Summary

The four Greeks quantify how an option's price reacts to stock moves, volatility, and the passage of time.

Why Greeks matter

The price of an option changes for four separable reasons: the underlying stock moves (delta), the rate at which delta itself changes (gamma), time passes (theta), and implied volatility shifts (vega). The Greeks are just the partial derivatives of the Black-Scholes pricing formula — but you don't need the calculus to use them. You need to know which Greek dominates your position at each point in time.

Delta — directional exposure

Delta is the expected change in the option's price for a $1 move in the underlying. An at-the-money call has a delta near 0.50 — meaning if the stock rises $1, the call rises about $0.50. Delta also approximates the probability the option expires in-the-money, which is why traders use 30-delta and 15-delta strikes as shorthand for likelihood.

Gamma — how fast delta changes

Gamma is highest for at-the-money options close to expiration. It's what makes gamma-squeeze headlines during meme-stock rallies: dealers who sold calls have to hedge more and more aggressively as delta climbs, buying the underlying and pushing price further up.

Theta — the ticking clock

Theta is time decay, expressed as dollars lost per day. A 30-day at-the-money call might lose $5 per day and $12 per day in its final week. Long options are constantly bleeding theta; short options collect it. This is why option sellers can profit even when the stock barely moves.

Vega — volatility sensitivity

Vega measures how much the option's price changes for a one-point move in implied volatility. Before an earnings report, IV rips higher and every option — call and put — gets more expensive. After earnings, IV collapses ("IV crush") and even a correct directional bet can lose money if you paid for inflated volatility going in.

> Every option position is really four separate bets: on direction, on the speed of that direction, on time, and on volatility.

(Educational simulation only — not financial advice. Practice everything below with $100,000 virtual cash on TradeHQ.)

Key takeaways

• Delta ≈ how much the option moves per $1 stock move (and roughly = probability of finishing ITM).
• Gamma is highest at-the-money and near expiration.
• Theta bleeds long options daily; sellers collect it.
• Vega spikes before earnings and collapses immediately after ("IV crush").

Check your understanding

• What does theta measure? Options: Directional exposure; Time decay per day; Volatility sensitivity; Interest-rate risk. Correct answer: Time decay per day. Why: Theta is the dollar amount an option loses per day from time decay.
• An at-the-money 30-day call option has a delta close to: Options: 0.10; 0.30; 0.50; 0.90. Correct answer: 0.50. Why: ATM options have deltas near 0.50 — a roughly 50/50 chance of finishing ITM.
• 'IV crush' typically happens: Options: Right before earnings; Right after earnings; On Fed decision day; At market open. Correct answer: Right after earnings. Why: IV inflates before earnings and collapses immediately after the release.
• Which Greek measures the rate of change of delta? Options: Vega; Theta; Gamma; Rho. Correct answer: Gamma. Why: Gamma tells you how quickly delta itself changes.

Sources

• Investopedia — Option Greeks (https://www.investopedia.com/trading/getting-to-know-the-greeks/)
• Cboe — The Greeks (https://www.cboe.com/education/tools/)

Practise this lesson

Open the practice desk and apply this lesson immediately with $100,000 in virtual cash. Concepts become usable when they are rehearsed under simulated conditions, not when they are read. Educational simulation only — not financial advice.