The Option Greeks Explained - Delta, Gamma, Theta and Vega

Reviewed by Leon Moyer - Published October 9, 2026 - Last reviewed October 9, 2026

The option Greeks are measurements of how much an option's price is expected to change when one thing about it changes: the stock price (delta), the speed at which delta itself changes (gamma), the passage of time (theta), or implied volatility (vega). Most translate directly into dollars.

In the first lessons of this course you worked out what options are worth at expiration, when only the stock price matters. Before expiration, its price moves for several reasons at once. As Call Options Explained warned, a call can even lose value while the stock rises. The Greeks help estimate the contribution of each input to that movement.

What do the option Greeks measure?

Each Greek answers one "what if" question while holding everything else constant:

The Greeks come from an option pricing model. This module uses Black-Scholes, which here takes five inputs: the stock price, the strike, the time to expiration, implied volatility and the interest rate (dividends are set to zero here). Nudge one input, measure how far the model's price moves, and you have a Greek. Every number in this module comes from that model, the same one the free OptionsPro profit calculator runs.

These are hypothetical European-style options on a stock paying no dividends, with a standard 100-share multiplier. The model ignores fees and spreads. Real U.S. equity options allow early exercise, and brokers' models may account for it and for dividends, so their Greeks can differ. See OIC on pricing models.

What are the Greeks of an example option?

Here is the example the whole module uses. XYZ trades at $50. The XYZ 50 call expires in 30 days, implied volatility is 30% and the interest rate is 4.5%. The model values the call at $1.81 per share, or $181 for one contract.

The card shows the Greeks per contract, as the calculator does. An options chain would quote the same call per share: a delta of 0.53, gamma of 0.09, theta of -$0.03 and vega of $0.06. For one contract (100 shares):

• Delta +53.43: if XYZ rises $1, the call gains about $53.43. If XYZ falls $1, it loses about the same.
• Gamma +9.24: after that $1 rise, delta itself climbs by about 9, to about 62 (0.62 per share), so the next dollar is worth more than the first.
• Theta -$3.16: each day that passes with nothing else changing costs the call about $3.16.
• Vega +$5.70: if implied volatility rises one point, from 30% to 31%, the call gains about $5.70.

Rounding per share hides detail: a theta quoted as -$0.03 is really -$0.0316, or $3.16 per contract, not $3.00.

How do you use the Greeks to estimate an option's price?

For a small move over a short period, you can add the Greeks to estimate the change in one contract's model value: delta x the stock's move + half of gamma x the move squared + theta x the days passed + vega x the change in implied volatility. Use per-contract Greeks and measure the IV change in percentage points. This example holds interest rates fixed.

For small moves over short periods, the Greeks are remarkably accurate. For large moves or long stretches the estimate drifts, because the Greeks themselves change as the inputs move.

Why doesn't the payoff chart show the Greeks?

A payoff chart shows only expiration day. For this call it is the familiar hockey stick: a flat $181 loss at or below $50, break-even at $51.81, and $100 more for every $1 above that.

The Greeks describe the path before that day. With XYZ at $50 and 30 days left the call is worth $181, yet at expiration with XYZ still at $50 it would be worth nothing. Theta measures how fast that gap closes, delta and gamma describe how the value bends as XYZ moves, and vega describes how the whole curve lifts or sinks when implied volatility changes.

What about rho?

Rho is the fifth Greek: how much an option's price changes when interest rates rise one percentage point. The XYZ 50 call's rho is about $0.02 per share, or $2.05 per contract. Rates rarely move a full point in a month, so rho barely matters for short-dated options. It grows with time to expiration (the same call with 90 days left has a rho of $6.10 per contract), so it matters more for options that expire a year or more out.

See OIC on rho.

What should you remember?

• They are estimates, not promises. They come from a model. Real option prices are set by buyers and sellers, and the model's implied volatility is itself backed out of those prices.
• They change constantly. Every stock move, day and IV shift changes them all.
• Sellers see the opposite signs. Someone who sells this call has a delta of -53.43 and has positive theta of about $3.16 per day, holding other inputs fixed. This is a sensitivity, not guaranteed income.
• Check the units. Know whether your platform shows per share, per contract or per position before comparing numbers.

Next, What Is Delta in Options? takes the first and most-used Greek and shows how it changes from one strike to the next.