The Greeks

An option's price never sits still. The market moves, the clock ticks, the mood swings — and the premium reacts to all of it at once. The Greeks are the names we give to those separate reactions, so you can talk about each one on its own instead of staring at a single number that wobbles for many reasons.

You don't need any calculus here. Each Greek answers one plain question: if one thing changes, how much does the option's price move? We'll take them one at a time, then end on the one — gamma — that the rest of this track is really about.

Delta: directional exposure

The first question is the obvious one. The market moves a little — how much does the option move with it?

That is delta. A delta of 0.50 means that for every $1 the underlying rises, the option gains about 50 cents. A call's delta runs from near 0 (far out of the money, barely reacting) up to near 1 (deep in the money, moving almost dollar-for-dollar with the market). A put's delta is negative, because a put gains value when the market falls.

A handy way to picture it: delta is the slope of the payoff line from the last lesson. Where the line is flat, delta is near zero — the option barely cares what the market does. Where the line rises steeply, delta is near one — the option tracks the market closely.

Hover the curve to read the P&L at any underlying price.

The same line

Here is that long call again. Delta is nothing more exotic than the slope of this line at the price the market sits at now.

Flat = low delta

Below the strike the line is nearly flat. A $1 move barely changes the option's value — delta is close to zero.

Steep = high delta

Above the strike the line climbs steeply. Now the option moves almost dollar-for-dollar with the market — delta is close to one.

Delta is slope

So delta just reads off how steep the line is right here. Gamma — the next Greek — is how fast that steepness itself changes as the market moves.

Look at that same long call. Below the strike the line is nearly flat (low delta); above it, the line climbs (high delta). Delta is just how steep that line is at the price the market is sitting at right now.

Gamma: how delta changes

Here's the catch. Delta itself isn't fixed. As the market moves, the slope of that payoff line changes — so delta changes too. The Greek that measures that is gamma.

Think of a car. Delta is your speed; gamma is your acceleration — how fast the speed itself is changing. An option with high gamma has a delta that flips quickly as the market moves: it can go from barely reacting to fully reacting over a small move in price.

Gamma is largest for options near the strike and close to expiry, because that's where a small move in the market makes the biggest difference to whether the option ends up worth something or nothing. The same 0DTE options from the last lesson carry the most gamma of all.

Hold on to gamma. When a dealer sells you that option, they inherit the opposite gamma — and managing it forces them to trade in a particular direction as the market moves. That mechanism is the whole point of the terminal, and we build it up over the next three lessons.

Theta: time decay

An option has a deadline. Every day that passes is one less day for the market to move in the option's favour — so the option quietly loses a little value just from time passing. That bleed is theta.

Think of an ice cube on a table. Even if nothing touches it, it shrinks a little every hour. Theta is the option melting as the clock runs down. A theta of -0.05 means the option loses about 5 cents of value per day, all else equal.

The melt isn't steady — it speeds up as expiry approaches, especially for at-the-money options. This is the mirror image of gamma: the same closeness to the strike and to expiry that makes gamma large also makes theta bite hard.

Vega: volatility sensitivity

The last reaction isn't about the market moving or the clock ticking — it's about how jumpy the market is expected to be. When traders expect bigger swings, options get more expensive, because a bigger expected range means a better chance the option finishes with value. Vega measures that sensitivity.

A vega of 0.10 means that if the market's expected swinginess rises by one point, the option's price rises by about 10 cents — even if the underlying hasn't moved at all. This "expected swinginess" is implied volatility, and it's important enough that the whole next lesson is about it.

Reading the line, not a recommendation

One thing to keep straight: none of the Greeks tell you what will happen. They describe how a contract responds to change — its direction, its acceleration, its decay, its sensitivity to mood. They're a vocabulary for mechanics, not a forecast and not advice.

What to carry forward

• Delta = directional exposure: price move per $1 move in the underlying.
• Gamma = how fast delta changes: the curvature, and the Greek that matters most here.
• Theta = time decay: value lost per day as expiry nears.
• Vega = volatility sensitivity: price change when expected swinginess changes.
• Every Greek a buyer holds, the seller holds in mirror image — that opposite side is where dealer hedging comes from.

Gamma is the thread. Next we pin down the volatility that vega reacts to — the difference between what the market expects and what actually happens.

Next step

Watch the greeks move.

Exposure aggregates delta and gamma across every strike so you can see where they concentrate.

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