Unit 8 of 15 · Intermediate

One position, all four greeks

In one read

The greeks are one dashboard, not four separate facts. On any single option they read together: delta is directional exposure, gamma is how fast that exposure changes, theta is what each day costs, and vega is exposure to changes in implied volatility. Reading them at once is the actual skill, because they pull against each other — a long option that carries positive gamma (it gets more directional as it moves your way) also carries negative theta (it bleeds value every quiet day), and the same contract's vega means an IV drop can hurt even when direction helps. This capstone takes the one generic at-the-money call carried through the delta, gamma, theta, and vega units and reads all four numbers on it simultaneously across a few scenarios, so the greeks stop being trivia and become a single instrument panel you scan before and during a position.

Four numbers, one dashboard

You have met the greeks one at a time. In a real position they are never one at a time — they are a single instrument panel you read all at once:

  • Delta — directional exposure (how much per $1 move).
  • Gamma — how fast that exposure changes.
  • Theta — what one day of waiting costs.
  • Vega — exposure to a change in implied volatility.

The skill is reading them together, because they pull against each other. The same long option that gives you positive gamma (it gets more directional as the move goes your way) charges you negative theta (it bleeds value every quiet day), and carries vega risk on top (an IV drop can cost you even when direction helps). No single greek is the position — the interaction is.

One worked position, read four ways at once

Here is the exact contract we have carried through the last four units: one long GENCO $100 call, a month to expiry, GENCO at $100. Its panel:

deltagammathetavega
0.500.08 / $1−$0.05 / day$0.12 / IV pt

Now read the whole panel across three scenarios:

  • GENCO rises $2 overnight, IV unchanged. Delta (~0.50) earns roughly +$1.00; gamma means delta is now ~0.66, so the position is more directional than it was; theta still quietly took ~$0.05. Net: direction won, and gamma made it win a little faster.
  • A quiet day, GENCO flat, IV unchanged. Delta and gamma do nothing; theta takes ~$0.05. Nothing happened to price and the position still cost you a day. That is the long option's standing rent.
  • GENCO rises $1 but IV falls 5 points. Delta earns ~+$0.50; vega loses ~5 × $0.12 = $0.60; theta takes another ~$0.05. You were right on direction and the panel is still red — vega and theta outweighed delta.

That third row is the entire reason to read all four at once. Any single greek would have lied to you about the day.

See it in kestrel

A four-greek panel is only as honest as the tape it is read against. Run a real session where price and volatility both move:

npx kestrel.markets sim s-p-500-etf-pandemic-volatility-crash

That runs a deterministic simulation over a generic broad-ETF session with real directional and volatility swings — managed licensed data, no wall time, no signup, no card — and prints a certified proof URL. Kestrel holds the option as a first-class position, so the interplay of the four greeks across the tape is something you recompute rather than narrate. Run it again on your own machine, byte for byte:

npx kestrel.markets certify https://kestrel.markets/proof/art_66d7dda7f0466f69c123463c

Keep the panel one command away: drop the kestrel.markets MCP server into your client and the next session opens where this one left off — no account in between.

Recompute it

Every claim in this unit recomputes from a certified proof — no account, no card.

/proof/art_66d7dda7f0466f69c123463c
Keep readingTheta: the price of time