What does delta mean in options?

Delta is the change in the option premium for a $1 move in the stock. A call with a delta of 0.35 gains about $0.35 per share, or $35 per contract, when the stock rises $1. Delta also serves as the share equivalent of the position, so one contract at 0.35 delta behaves roughly like owning 35 shares.

How do I calculate theta in dollars?

Multiply the quoted theta by 100. A theta of 0.05 means the contract loses about $5 of value per calendar day if nothing else changes. Over a seven day week that is $35, which on a $250 contract is 14 percent of the premium gone with the stock sitting still.

Which Greek matters most before an earnings report?

Vega, because implied volatility usually falls sharply once the announcement is out. Vega is a local estimate and it overstates the damage on a large move, so use it to rank positions rather than to forecast the loss. Repricing the position at the lower volatility level gives a far more honest number.

Why does gamma matter if I already know delta?

Delta is only accurate for a small move. Gamma tells you how fast delta itself changes, so it tells you how wrong your delta estimate becomes after a large one. Gamma is highest at the money and close to expiry, which is why short options in their final week can change character within hours.

Is a 0.30 delta the same as a 30 percent chance of expiring in the money?

It is an approximation traders use for strike selection and it is close enough for ranking one strike against another. It is not exact, because delta comes from the pricing model and is affected by dividends, interest rates and the volatility skew. Treat it as a sorting tool rather than a probability you would bet the account on.

Does rho ever matter for equity options?

Rarely for short dated contracts. A rho of 0.04 means a one percentage point change in interest rates moves the premium by about $4 per contract, and rates do not usually move a full point over a six week holding period. Rho becomes relevant for long dated options such as LEAPS, where the time value is large enough for the discount rate to show.

Option Greeks Explained: Delta, Gamma, Theta, Vega and Rho

Five numbers sit on the same chain line as the price. They are worth more than the price is. Each one is a rate of change: how the premium responds to the stock, to a day passing, to a shift in implied volatility, to interest rates. All five are quoted per share. Multiply by 100 to see the money.

Ranked by how much they actually move

One contract, used for everything below. A stock trades at $100. The $105 call expires in 42 days. It is quoted at $2.50, with implied volatility of 30%.

Greek	Quoted	Per contract	What it answers
Theta	-0.05	-$5 per day	Premium lost as one calendar day passes
Delta	0.35	$35	Premium change per $1 move in the stock
Vega	0.12	$12	Premium change per 1 point of implied volatility
Gamma	0.04	$4	Delta change per $1 move in the stock
Rho	0.04	$4	Premium change per 1 percentage point of rates

Textbooks run this list alphabetically or in order of Greek prestige. The order above is roughly how much each one will cost or make you on a $250 contract over six weeks, which is the ordering that changes decisions.

Theta, the only one whose sign you know in advance

Everything else on that table can go either way. Theta never does. A long option loses time value every single day. The only question is the rate.

weekly decay = $5 x 7 = $35

$35 a week on a $250 contract is 14% of the position. You are charged that for nothing happening. Across the full 42 days the entire $250 has to come from somewhere, because this contract is all extrinsic value and extrinsic value is contractually zero at expiry, which makes a short dated out of the money option an opinion rented by the day.

The rate is uneven. At the money options decay faster as expiry approaches, roughly in line with the square root of the time remaining, so the last fortnight costs more per day than the first fortnight did. Far out of the money options have little left to lose, so their theta flattens toward zero and they simply sit there being worthless in slow motion.

Long options pay the rent. Short options collect it. That is the entire economic argument behind covered calls and cash-secured puts.

Delta is a position size before it is a sensitivity

new premium = old premium + (delta x stock move)

The stock rises $1, to $101, and the call is worth about $2.50 + (0.35 x $1) = $2.85. The contract gains $35. Reverse the move and the arithmetic runs backwards.

The second use matters more and gets mentioned less.

share equivalent = delta x 100 x contracts

One contract at 0.35 delta behaves like 35 shares. Ten contracts behave like 350 shares. That is $35,000 of stock exposure controlled by $2,500 of premium, and it is the number to put into the sizing rules from risk management for traders, because it is what the position actually is. Traders who size by premium paid are sizing the deposit. The exposure is the thing that moves.

Delta runs from 0 to 1 for calls and 0 to -1 for puts. Deep in the money contracts approach 1. They track the stock nearly dollar for dollar. Far out of the money contracts approach 0 and stop responding to the stock almost entirely, which is what a $0.10 lottery ticket looks like from the inside.

Gamma, and why delta keeps lying to you

new delta = old delta + (gamma x stock move)

Stock to $101 and delta goes from 0.35 to about 0.39. Stock to $103 and delta is roughly 0.35 + (0.04 x 3) = 0.47, although gamma itself drifts as the stock travels, so that estimate degrades the further you push it. Gamma is a correction to delta. It needs a correction of its own. That is where I stop calculating by hand.

Gamma peaks at the money and climbs steeply into expiry. This $105 call carries 0.04 with 42 days left. The same strike with two days left and the stock at $105 can carry several times that, which means delta swinging from 0.30 to 0.70 inside a single session on a stock that moved 2%.

Position	Gamma sign	What a large move does
Long call or long put	Positive	Delta moves in your favour and gains accelerate
Short call or short put	Negative	Delta moves against you and losses accelerate

Across the chain the pattern is consistent, on the same underlying and the same expiry, across four strikes, all of them illustrative and rounded, and a live chain will argue with the second decimal place.

Strike, stock at $100	Delta	Gamma	Theta	Vega
$95 call, in the money	0.68	0.03	-$5	$10
$100 call, at the money	0.53	0.05	-$6	$13
$105 call, out of the money	0.35	0.04	-$5	$12
$115 call, far out of the money	0.09	0.02	-$2	$6

Gamma and vega both peak at the money, which is why at the money contracts react hardest to movement and to any repricing of volatility. As expiry approaches, gamma and theta rise while vega falls, so a contract bought as a volatility position quietly converts itself into a pure direction bet in its final week. Nobody sends a notification when that happens.

Vega, priced into an earnings date

Vega is the premium change per one point of implied volatility. This call carries 0.12. Implied volatility rising from 30% to 34% adds 4 x $0.12 = $0.48 per share. That is $48 per contract, with the stock frozen.

The cleanest demonstration is an earnings crush. Same stock at $100, earnings tomorrow, seven days to expiry. The $100 call and the $100 put together, a straddle struck at the money, price off 80% implied volatility: the call is $4.45, the put is $4.35, so the straddle costs $8.80, which is $880 for one of each.

Next morning the numbers are out. Implied volatility collapses to 40%, and a day has passed.

Input	Before	After
Implied volatility	80%	40%
Days to expiry	7	6
Stock	$100.00	$100.00
Straddle	$8.80	about $4.10
Position	$880	about $410

The straddle loses roughly $470, or about 53% of its cost. The stock is exactly where it started.

Now the part I find genuinely useful. The straddle carries vega of roughly 0.22, so the linear estimate of a 40 point volatility drop is 40 x $0.22 x 100 = $880, which is the entire position. Repricing the contracts properly gives $470. Vega overstated the damage by almost double, because vega itself shrinks as implied volatility falls, and the Greek does not know that about itself. Every Greek on your screen is a derivative taken at one instant. It is honest only for small changes. For a 40 point move in implied volatility, reprice the position.

Rho gets a paragraph, and the paragraph is generous. Rho of 0.04 means a one percentage point change in rates is worth about $4 on this contract, and rates rarely travel a full point inside six weeks. It becomes real on two year contracts, where there is enough time value for the discount rate to bite, through the channel described in how interest rates affect stocks.

Where the model quits

The Greeks come out of a pricing model that assumes one volatility number and continuous price paths. Real stocks gap. A model reporting 0.12 delta on your short call has nothing to say about a takeover announcement that reopens the stock 30% higher. No Greek prices that event. The model it comes from does not believe in it.

They are also stale by construction. Delta changes as the stock moves, vega changes as time passes, and the whole row updates every time a quote does, so treat them as accurate for small changes over short periods, roughly directional over medium ones, and decorative in a crisis.

Next: implied volatility explained for where the vega input comes from and how to judge whether it is high, and vertical spreads explained for structures whose Greeks are bounded on both sides. The option Greeks quiz checks whether the arithmetic stuck.