Options Primer Part 4: The Greeks

WidgetCo drops $5 tomorrow. How much do you lose?

It depends. On where the stock started. On how much time is left. On whether volatility spiked with the drop. On how far away your strike is. The answer is a function of all these variables at once.

The Greeks are tools for navigating this. But to understand what they’re actually measuring, we need to talk about the surface your option lives on.

The pricing surface

An option’s price depends on several inputs: stock price, time to expiration, implied volatility. Strike is fixed when you buy. That leaves three moving variables - which means the full picture is four-dimensional (three inputs plus price). There’s no way to draw that.

But we can take lower dimensional slices. Hold IV constant and look at how price changes with stock and time. That’s a surface:

Drag to rotate. This is a $50 call with IV fixed at 45% - one slice of the larger space.

Hold time constant too, and we get a 2d curve:

Same option, but now we’re only watching how price changes with stock. We’ll use both views throughout.

Back to the surface: see those colored dots with arrows? Each dot is an option at a different position. The arrows show which way you’re exposed - how the option responds when things change, or when your option moves across the surface.

Those arrows are the Greeks. They work in the full space too, pointing in directions we can’t draw.

Delta - stock price sensitivity

Delta measures how much your option moves when the stock moves $1. It’s the most immediate question: if WidgetCo goes up $1 tomorrow, how much do I make?

You buy a $50 call, 30 days to expiration. It costs $2.85. Delta is 0.52.

If WidgetCo goes from $50 to $51, your call gains roughly $0.52. If WidgetCo drops from $50 to $49, your call loses roughly $0.52.

Drag the stock price. Watch how the blue tangent line (delta) changes slope as you move.

Delta ranges from 0 to 1 for calls. Deep out of the money (stock way below strike), delta is near 0. At the money (stock at strike), delta is around 0.5. Deep in the money (stock way above strike), delta approaches 1 - moving almost 1:1 with the stock.

For puts, delta is negative - ranging from -1 to 0. A put with delta -0.5 gains $0.50 when the stock drops $1.

Another way to think about it: delta is how much stock you effectively own. A 0.52 delta call on 100 shares behaves like owning 52 shares. You paid $285, not $5,000 - the option amplifies your capital while exposing you to 52 shares worth of movement.

Theta - time decay

Every day, your option loses value. That’s theta.

Your $50 call has theta of -0.08. You’re losing $0.08 per share per day - $8 per contract - just by holding it.

Why? An option is a bet that something will happen before a deadline. The value of that bet depends on how much time is left for it to play out. With 30 days, anything could happen. With 1 day, much less likely.

Drag the time slider. Watch how the red tangent line (theta) steepens as expiration approaches.

Theta accelerates near expiration. With 30 days left, you lose $8/day. With 7 days left, you might lose $15/day. At 30 days, losing one day costs you 1/30th of your remaining time. At 7 days, losing one day costs you 1/7th. Same absolute time, bigger percentage hit.

Here’s what theta feels like in practice: You buy a call. The stock does nothing for a week. You check your position. It’s down 5%.

Gamma - delta’s rate of change

Delta isn’t constant. It changes as the stock moves.

That’s gamma - how fast delta changes per $1 stock move.

Your $50 call has delta 0.52 and gamma 0.04.

If WidgetCo goes from $50 to $51:

• Your call gains $0.52 (from delta)
• Your new delta is 0.56 (old delta + gamma)

If it continues to $52:

• You gain roughly $0.56 on that dollar (using your new delta)
• New delta is 0.60

Move the stock price. Watch how the purple tangent line (gamma) shows whether delta is accelerating or decelerating.

Why care? Gamma tells you how unstable your exposure is. High gamma means your delta can flip quickly. At $50, your call has delta 0.52 - you’re moderately exposed. But gamma is high. If the stock moves $5, your delta might be 0.75 or 0.25 depending on direction.

Low gamma means stability. Deep ITM, delta is 0.95 and gamma is tiny. The stock can move $5 and delta barely changes - you’re locked in at near-1:1 exposure.

Vega - volatility sensitivity

Vega measures how much your option moves when IV changes by 1 percentage point.

Why does IV matter? Remember: IV is the market’s estimate of how much the stock might move. Higher IV means bigger expected swings. Options are bets on movement - if bigger moves are expected, your option is worth more. When IV drops, the market is saying “actually, calmer than we thought” - and your option loses value because the big move you were betting on now seems less likely.

Your $50 call has vega of 0.08. If IV goes from 45% to 46%, your call gains $0.08 per share - $8 per contract.

Drag the IV slider. Watch how the green tangent line (vega) shows sensitivity to volatility changes.

This is what makes earnings plays tricky. Before earnings, IV is high - uncertainty is priced in. After earnings, uncertainty resolves, IV collapses. You can be right about direction and still lose because IV dropped faster than the stock moved.

Back to the surface

Those arrows from the first surface:

Now you can read them.

Each point has two arrows: blue (delta) points along stock price, red dashed (theta) points toward expiration.

Calm waters (top left) - ATM, 45 days out. Both arrows moderate length. You have time, you have exposure.

The cliff (bottom left) - ATM, 5 days out. The red theta arrow is longer - time decay is accelerating. The blue delta arrow is similar - stock sensitivity hasn’t changed much.

Deep ITM (right side) - $12 above strike, 30 days out. The blue delta arrow is long - this option moves nearly 1:1 with stock.

How they interact

The Greeks don’t operate in isolation. On any given day, all of them are working simultaneously.

Drag the point around. Watch delta and theta change as you move across the surface. Near expiration (the cliff), theta accelerates. Deep in the money, delta approaches 1. At the money with time left, you’re in the sweet spot - moderate exposure to everything.

Greek summary

When you’re long options: delta is your directional bet, gamma means big moves help you, theta works against you, vega helps on IV spikes.

When you’re short options, the signs flip. Theta works for you. Vega works against you. That’s Part 5.

What the Greeks don’t tell you

The Greeks are local. They tell you what happens for small moves right now. They don’t tell you which direction the stock moves, what IV will do, or how big the move will be.

You can have perfect Greek management and still lose money because the stock went the wrong way.

Part 5: you stop buying options and start selling them.

This is Part 4 of a 5-part series on options. Part 3 covers volatility. Part 5 covers selling options.