The Greeks in plain English: four dials, no formulas

Four questions, not four formulas

The Greeks are taught badly almost everywhere, and the reason is a choice of framing. They are presented as properties of an option — facts to memorise about a contract — when they are nothing of the sort. Every one of them is the answer to a question you would ask anyway.

You own a position. You want to know: what happens if the stock moves? What happens if a day goes by and nothing else does? What happens if the market gets frightened? Those are not advanced questions. They are the only three questions there are, and the Greeks are the answers with Greek letters stapled on.

Delta: what if the shares move a dollar?

A delta of 0.30 means that if the shares move $1, the contract’s price moves about 30 cents. That is the whole definition. It is a rate of exchange between the stock and the contract.

Delta is small when the price you agreed to is far from today’s — the contract barely reacts, because a dollar does not change whether such a distant price gets reached. It is large when your agreed price is close, because then a dollar genuinely might. At the extreme, a contract certain to be used behaves exactly like 100 shares, and its delta is 1.00.

There is a second reading, and in practice it is the one traders use out loud: delta doubles as rough odds. A delta of 0.30 is loosely a 30% chance the agreed price comes into play by the deadline. It is approximate — the exact relationship is the business of the lesson on where the percentage comes from — but it is close enough that “I sell 0.20 deltas” is a meaningful sentence about how often you expect to be called upon.

Where you meet it in this app: Compare strikes prints the delta on every contract it lists, and lets you filter by it directly, labelled as how likely the shares are to reach your price. Choosing a lower band is choosing a price further away: safer, and it pays less. That trade-off is the only thing that filter does.

Theta: what if a day passes?

An option is a promise with a deadline, and part of what the buyer pays for is simply the time remaining. Every day that passes, there is less time left for anything to happen, so that part of the price erodes. Theta is how much erodes per day.

If you bought the contract, this is a tax on patience. If you sold it — which is every strategy in this app — the erosion is your income. You were paid up front for a promise, and each quiet day makes that promise cheaper to buy back. A theta of $8 means roughly $8 a day is working in your favour, as long as nothing else happens.

The decay is not steady, which the curve shows: it is gentle far out and steepest in the last stretch before the deadline. That looks like an argument for only ever selling very short contracts, and it is the most seductive wrong conclusion in options. The same final stretch where income arrives fastest is where the risk arrives fastest, for the reason the next section is about.

Vega: what if the market gets nervous?

Option prices contain a judgement about how far the stock might move. When traders collectively expect bigger swings, every option on that stock gets more expensive — including the one you already sold. Vega is how much the contract’s price moves when that collective expectation shifts.

This is the dial that produces the single most common beginner complaint, and it sounds like a bug:

I was right about the stock. It didn’t move. I’m still down on the week.

Nothing is broken. Somewhere in the world something frightened the market — a different company’s results, a central bank, a headline — and the price of swings went up everywhere. The contract you sold for $90 now costs $130 to buy back, on a stock that closed the week exactly where it opened. If you hold to the deadline and the shares stay put, that unrealised loss evaporates and you keep the $90. If you need to close early, it is entirely real.

Gamma: what happens to delta?

Three dials down, one oddity left. Gamma is not about the contract’s price at all — it is about delta. It answers: when the shares move a dollar, how much does my sensitivity to the next dollar change?

A position with low gamma is a position whose character is stable. One with high gamma changes what it is while you watch. A contract that was barely reacting to the stock can become one that tracks it almost dollar for dollar inside a single session, and that transformation is what turns a comfortable trade into a full loss faster than most people can decide what to do.

Gamma is nearly flat for most of a contract’s life and spikes in the final week or two. That is why this app refuses to start a trade inside that window at all, however good the income looks there. The lesson on why we won’t sell you an option expiring next week is four minutes and is really a lesson about this one dial.

The whole set on one page

Read the middle column as a question and the right-hand column as what it means for someone who has sold an option, which is the side every strategy here puts you on.

Three against one looks grim stated that way, and it is worth sitting with rather than softening: as a seller you are paid one way and exposed three. The payment has to be large enough to cover all three, which is exactly the judgement a high win rate does not make for you.

Which two you actually need on day one

A promise, since lessons like this one usually end by implying all four are homework. They are not, and for someone selling cash-secured puts a fortnight or more from expiry the honest priority is clear.

• Delta — learn it properly. It is the one you will actually set. Reading it as rough odds is enough to make every screen in this app legible.
• Theta — know it is on your side. You do not need to track the number. You need to understand that quiet, boring days are the business working, because that belief is what stops people closing good trades out of impatience.
• Vega — know it exists, so it doesn’t frighten you. Its whole practical value to a beginner is having an explanation ready the first time a position shows a loss on a day the stock did nothing.
• Gamma — let the rules handle it. It mostly matters in the final fortnight, and nothing here will start a trade there. If you ever disable that floor yourself, gamma stops being trivia and becomes the most important dial on the page.

Where to go next

You can now read every number on every screen here. The natural next step is the reason the strategy works at all: implied versus realized volatility — which is a lesson about vega, told from the business end.

Every term here is also defined on its own in the glossary, and any word with a dotted underline anywhere in the app will explain itself if you tap it.