The option greeks in plain words · Options 101

In this lesson

Use delta, gamma, theta, and vega to estimate price changes, and use delta as a rough guide when choosing strikes.

6
short parts: 12
questions: ~15
minutes

Read the whole lesson on one page

The greeks in plain words, and strike choice: the lesson

Four dials, not one number

An option's price reacts to the stock price, to time passing, and to implied volatility. The Greeks put a number on each reaction.

Delta: the stock price.
Gamma: how fast delta changes.
Theta: time passing.
Vega: implied volatility.

Delta: price change per $1

Delta of a 50 call as the stock moves, IV 30% and 30 days left. It runs from near 0 far below the strike to near 1 far above it, and is about 0.5 at the strike.

Model values, not real quotes.

Step 1: A call at 3.00 with delta 0.60: the stock rises $1, so the call gains about 0.60 a share.
Step 2: Per contract: 0.60 × 100 = about +$60.
Step 3: A put with delta −0.25: the stock rises $2, so the put loses about 0.50 a share.

Gamma: delta isn't fixed

Delta changes as the stock moves. Gamma is how fast. Close to expiration, an at-the-money option's delta can swing from near 0 to near 1 across a few dollars.

30 days left
3 days left

Delta of a 50 call at 30 days and at 3 days to expiration, IV 30%. The 3-day line is much steeper around 50, which is gamma.

Model values, not real quotes.

Theta and vega

Theta	Vega
Time passing	Implied volatility
Per day, in price per share	Per 1 point of IV, in price per share
50 call here: about −0.03 a day	50 call here: about 0.06 per point
Hurts the buyer, helps the seller	Hurts the buyer if IV falls

Putting the dials together

Estimate tomorrow for the 50 call. Say the stock rises $1 and IV falls 2 points.

Step 1: Delta: +0.52 × $1 = +0.52.
Step 2: Theta: one day of decay = −0.03.
Step 3: Vega: −2 points × 0.06 = −0.12.
Step 4: Total: +0.37, so 1.72 becomes about 2.09, or about +$37 per contract.

Delta as a guide to strikes

50 call (delta 0.52)	55 call (delta 0.14)
Moves about 0.52 for a $1 stock move	Moves about 0.14 for a $1 stock move
More like owning the stock	More like a lottery ticket
Costs 1.72	Costs 0.30

Worked example: Three calls on a $50 stock, 30 days out (IV 30%)

Illustrative numbers, not real quotes.

Here is each call's price and its Greeks, per share:

	45 call	50 call	55 call
Price	5.22	1.72	0.30
Delta (approx.)	0.90	0.52	0.14
Per-contract change for +$1	about +$90	about +$52	about +$14
Gamma (delta change per +$1)	about +0.04	about +0.09	about +0.06
Theta (per day)	about −0.01	about −0.03	about −0.02
Vega (per 1 IV point)	about 0.03	about 0.06	about 0.03
Breakeven at expiration	50.22	51.72	55.30

Now use the 50 call to estimate tomorrow. Say the stock rises $1 and IV falls 2 points:

Delta: +0.52 × $1 = +0.52.
Theta: one day of decay = −0.03.
Vega: −2 points × 0.06 = −0.12.
Total: +0.52 − 0.03 − 0.12 = +0.37, so 1.72 becomes about 2.09. Per contract, that is about +$37.
The estimate runs a little low because delta rises as the stock rises. That is gamma at work.

Education only, not investment advice. Options involve risk. Read the OCC's Characteristics and Risks of Standardized Options. Example numbers are illustrative.