The Option Greeks: Delta, Gamma, Theta, Vega and Rho

Michael Whitman · Trading since 2017, full-time since 2020 · Published 2026-09-26

The option greeks turn an option’s price into parts you can reason about one at a time. Each greek answers a single question of the form “if this one input moves a little and nothing else does, how much does the option’s price change?”

There are five that matter to most traders. Each has its own page on this site, so this one is the map: what each greek measures, how they relate, and what all five looked like on one real chain.

How it works

An option’s price depends on five inputs: the stock price, the strike, the time left, the expected volatility, and interest rates (plus dividends for stocks that pay them). A pricing model, usually from the Black-Scholes family, turns those inputs into a fair value. Each greek is the slope of that value with respect to one input.

Delta is the change in the option’s price for a $1 move in the stock. A call’s delta runs from 0 to 1 and a put’s from -1 to 0. Delta has the full treatment, including why it is often read, loosely, as a rough chance of finishing in the money.

Gamma is the change in delta for a $1 move in the stock. It is highest for options near the money and close to expiry, which is why gamma is the greek that makes a quiet position suddenly fast.

Theta is the change in price for one day passing. It is negative for almost every option you buy, because a day less to expiry means less time for a move. Theta covers the shape of that decay.

Vega is the change in price for a one-point move in implied volatility. It explains why an option can lose value on a day the stock moved the right way, the effect the IV crush page measures around earnings. Vega has the detail.

Rho is the change in price for a one-point move in interest rates. It is small on short options and grows with time, so it is the greek most people skip until they hold something a year or more out.

All five are quoted per share. A standard US stock or ETF option covers 100 shares, so multiply by 100 to get dollars per contract.

The five greeks at a glance

Read the columns as pairs. Gamma and theta peak in the same place, near the money and near expiry. That is the trade-off at the center of short-dated options: the position that reacts fastest to the stock is also the one losing the most each day to the clock.

Vega and rho peak in the opposite corner, far from expiry. A long-dated option is mostly a position on volatility and time, with less of its day-to-day price explained by the stock than its size suggests.

Beyond these five there are higher-order greeks, such as color, which tracks how gamma changes as time passes. They matter to market makers hedging large books and rarely to someone holding a few contracts.

A worked example

Take one real contract: the SPY call with a $771 strike expiring 16 Oct 2026, 21 days out. After the 25 Sep 2026 close, with SPY at $771.35, Cboe’s delayed quote showed a bid of $9.71 and an ask of $9.75, a midpoint of $9.73, and implied volatility of 11.70%.

Its greeks were delta 0.5446, gamma 0.0182, theta -0.2069, vega 0.7340 and rho 0.2361.

Now ask a question with all of them at once. Suppose SPY rises $5 over the next trading day while implied volatility falls by one point. The greeks estimate the change in the option’s price:

• Delta: 0.5446 x $5 = +$2.7230
• Gamma: 0.5 x 0.0182 x $5 x $5 = +$0.2275
• Theta: one day = -$0.2069
• Vega: 0.7340 x (-1 point) = -$0.7340

The total is about +$2.01 a share, or $200.96 on one contract. Delta did most of the work, gamma added a little because delta rose during the move, and time plus lower volatility took back about $0.94 of it.

After the move, delta would be about 0.6356 (0.5446 + 0.0182 x 5). The same contract is now more sensitive to the next dollar than it was to the first.

The quiet day is the other half of the lesson. If SPY closes flat and volatility does not move, theta alone says the contract loses about $20.69. That is the cost of waiting, paid every calendar day whether the market is open or not.

This is an estimate, not a result. It uses the greeks as they stood on one evening, and a real day moves all five inputs at once.

Rho, the greek that gets skipped

Rho is small on the options most people trade. On the 7-day SPY call it was 0.0778, 1.5% of the contract’s $5.26 midpoint, so a full point of rates would move the price by under 8 cents a share, or $7.78 on one contract.

It is not small on long-dated contracts. The call expiring 15 Dec 2028, 812 days out, had a rho of 8.9931 on a midpoint of $123.24. A one-point change in rates would move that price by about 7.3%, or roughly $899 on one contract.

That matters because rates do move by a point. Anyone holding long-dated calls through a stretch of changing interest rates has a position in rates as well as in the stock. Puts carry negative rho, so the same rate rise works against a long put.

The original data

What the five greeks look like across time, on one chain. These figures come from Cboe’s delayed quotes for SPY saved after the close on 25 Sep 2026: 13,290 contracts across 32 expiry dates, from that day out to 19 Jan 2029.

For each expiry below, the call is the listed strike closest to the $771.35 close. Theta is dollars per calendar day, vega is dollars per volatility point, and rho is dollars per rate point, all per share and exactly as Cboe published them.

Gamma falls as expiry moves out. At 7 days it was 0.0328, and at 812 days 0.0016, 20.5 times smaller. Theta follows the same path in dollars, from -$0.3554 a day to -$0.0342.

Vega and rho rise instead. Vega went from 0.4252 to 3.9890, 9.4 times larger, and rho from 0.0778 to 8.9931. The at-the-money call also carries more delta the further out it goes, from 0.5328 to 0.6968.

The same evening’s put at the 16 Oct $771 strike had a delta of -0.4698. Add the call’s 0.5446 and the two come to about 1.01, close to the 1 that put-call parity implies for a call and a put at the same strike and expiry.

All 14 rows, calls and puts, are in the greeks table for this page.

Demand for the topic is real. Of the 24,971 unique videos in this site’s search study, 8 have “greeks” or “option greek” in the title, from 8 different channels, at a median of 84,658 views.

When it fails

The greeks describe a small move with everything else frozen. Real markets move the stock, volatility and time together, and often by more than “small”. A $20 move in SPY is far outside the range where one gamma figure holds, because gamma itself changes along the way.

They are model outputs, not quotes. Cboe’s figures come from a model fed with its own implied volatility and rate assumptions. A different data vendor can show a slightly different delta for the same contract on the same evening, and neither is wrong.

Implied volatility is the weak input. Vega tells you what a one-point change does, not whether the change will be one point or ten. Around earnings or a Fed meeting, the volatility move can outweigh everything delta was expected to earn.

Theta is quoted per calendar day, and the market is not open every day. Two days of it pass between a Friday close and a Monday open with no trading in between, so a Monday change is easy to misread as a move in the stock or in volatility when part of it is the calendar.

Near expiry, the greeks become unstable. In the last day or two, gamma on an at-the-money option can swing delta from near 0 to near 1 on a small move, which is why 0DTE options behave so differently from monthly ones.

Adding greeks across positions only works with the same underlying. Summing delta across SPY and a single stock gives a number with no meaning, because a $1 move in each is not the same event.

Related

Each greek has its own page with the model shape behind it: delta, gamma, theta and vega. The options page covers calls and puts from the start, and options expiry explains what happens on the last day, when these numbers change fastest.

For what the greeks mean in practice, options trading mistakes puts theta and the bid-ask spread next to real SPY quotes. Gamma exposure shows how dealers’ combined gamma can shape a whole market’s day.

This page is educational, not financial advice. Test every idea on your own charts before risking money.