Options 04 · Options

The Greeks

Delta, gamma, theta and vega — four numbers that describe how a contract behaves

The Greeks are not advanced maths. They are four sensitivity readings — how much the contract's price changes when one thing about the world changes. You do not need to calculate them. You need to know which one is working against you.

Delta

A 0.50 delta call gains about $0.50 for every $1 the stock rises, which is $50 per contract. A 0.20 delta call gains about $0.20. Deep in-the-money options approach a delta of 1.00 and track the stock nearly dollar for dollar; far out-of-the-money options approach zero and barely respond at all.

Delta's second job is the more useful one for a beginner. Read it as an approximate probability: a 0.28 delta contract has roughly a 28% chance of expiring in the money. That reframes 'this call is only $115' into 'the market gives this a 28% chance', which is a much harder thing to talk yourself into.

Gamma

Gamma is the rate of change of delta. If delta is speed, gamma is acceleration. A contract with high gamma sees its delta rise quickly as the stock moves in its favour — the position gets more powerful as it works.

Gamma is highest at the money and rises sharply as expiration approaches, which is the mechanical reason short-dated at-the-money contracts move so violently. It is also, much later, the mechanism behind dealer hedging and gamma exposure — the advanced module at the end of this playbook.

Theta

Theta is the daily cost of holding. A theta of −0.06 means the contract loses about $6 per day, every day, if nothing else changes. It is the rent you pay on the position, and it is charged whether or not the stock does anything.

Decay is not linear. It accelerates as expiration approaches, and in the final week an at-the-money contract can lose value alarmingly fast. This is why 'it will come back' is a much worse argument for an option than it is for a share: the share has no deadline, and the option is being billed daily for having one.

Vega

Vega measures the effect of changing expectations. A vega of 0.08 means the contract gains about $8 for every one-point rise in implied volatility, and loses about $8 for every point it falls.

This is the Greek beginners never see coming, because it has nothing to do with the stock's price. Volatility expectations can collapse while the stock rises, and your contract loses money in a green market for reasons no price chart will explain. Module O5 is entirely about that.

How they interact — the honest summary

1. Delta is what you are buying

   Directional exposure. Everything else is the cost or the risk attached to holding it.

2. Theta is what you are paying

   Continuously, and faster near the end.

3. Vega is the risk you did not choose

   It can hand you a loss on a correct call or a profit on a wrong one.

4. Gamma is why short-dated contracts feel wild

   Delta changing fast makes the P&L swing far more than the stock's move suggests.