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

Greeks are model-based sensitivities to inputs, holding other inputs fixed. Delta describes underlying-price sensitivity; gamma describes a change in delta; theta describes time sensitivity; vega describes implied-volatility sensitivity. Interest rates and dividends can also matter. Finite market moves need not equal a first-order estimate, and different pricing models can produce different values.

Delta — directional exposure

A delta of 0.50 per share describes an approximate $0.50 option-price change for a $1 underlying move, with other inputs held fixed. For a 100-share contract that is about $50, before gamma and other effects. Some traders use delta as a rough probability shorthand, but it is not a calibrated real-world probability and need not match the model probability of finishing in the money.

Gamma — how fast delta changes

Gamma measures how delta changes as the underlying moves. It is often relatively large near the strike close to expiry, depending on volatility and other inputs. Dealer hedging can affect demand, but a chart or open-interest figure alone does not establish dealer positions, required hedges or the cause of a price move.

Theta — the ticking clock

Theta estimates an option value change as time passes under a model, holding other inputs fixed. State whether the quote is per share or per contract and whether a calendar or trading-day convention is used. Purchased options commonly have negative theta, but realised profit also depends on price, volatility and costs. Selling premium is not a guaranteed collection of that estimate.

Vega — volatility sensitivity

Vega estimates sensitivity to a one-percentage-point change in implied volatility, with other inputs held fixed. Implied volatility can change around earnings, but it need not rise before every release or fall afterwards. A long option can lose despite a favorable underlying move if time decay and a volatility decline offset that move.

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

(Educational only — not financial advice. TradeHQ offers $100,000 virtual cash for supported spot instruments. Options contracts, Greeks, futures margin and settlement are conceptual exercises; the simulator does not execute them.)

Key takeaways

• Delta estimates underlying-price sensitivity, not a guaranteed payoff or real-world event probability.
• Gamma is often relatively large near the strike close to expiration; volatility and other model inputs also matter.
• Theta is a model sensitivity; other price changes can offset or exceed it.
• Vega measures volatility sensitivity; a change in implied volatility is a different quantity.

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 a model estimate of time sensitivity with other inputs held fixed; units and time conventions must be stated.
• In the lesson example, a 0.50 delta and a $1 underlying rise imply approximately what change per option share, before other effects? Options: $0.10; $0.30; $0.50; $0.90. Correct answer: $0.50. Why: 0.50 × $1 = $0.50 per share, holding other inputs fixed; this is not an event probability.
• 'IV crush' typically happens: Options: Right before earnings; Right after earnings; On Fed decision day; At market open. Correct answer: Right after earnings. Why: A post-announcement drop in implied volatility is often called IV crush; it is not inevitable after every 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

• OIC — Delta (https://www.optionseducation.org/advancedconcepts/delta)
• OIC — Theta (https://www.optionseducation.org/advancedconcepts/theta)
• OIC — Vega (https://www.optionseducation.org/advancedconcepts/vega)
• Cboe — The Greeks (https://www.cboe.com/education/tools/)

Practise this lesson

Use $100,000 in virtual cash to practise supported spot instruments and general habits such as recording a trade thesis. Options contracts, Greeks, futures margin and daily settlement are conceptual exercises: calculate their examples in a worksheet, because TradeHQ does not execute derivatives contracts. Educational simulation only — not financial advice.