Delta, theta, vega and implied volatility
The Greeks are local approximations of how premium changes with price, time and volatility.
Options risk. Long options can lose 100% of the premium; short options can lose far more and may be assigned early. Examples use synthetic prices and the common 100-share multiplier — check actual contract terms.
What each measures
Delta: approximate change in option price per $1 change in the stock. Calls 0 to +1, puts −1 to 0. A 0.40-delta call gains about 0.40 per share (≈$40 per contract) for a $1 rise.
Theta: approximate change per day from time decay, usually negative for long options. −0.05 means about −$5 per contract per day, all else equal.
Vega: change per 1 percentage-point change in implied volatility. Implied volatility (IV) is the market's priced-in expectation of future movement — not a forecast of direction.
Greeks change as conditions change (gamma describes how delta changes). Use them for small moves; large moves need re-estimation.
IV crush
Before known events like earnings, IV is often elevated. After the event it commonly drops, cutting premium even if the stock moves in your favour.
Worked example
Combining Greeks (synthetic)
- Call at 3.00 with delta 0.50, theta −0.06, vega 0.08. IV falls from 60% to 40% after earnings; stock rises $1; one day passes.
- Delta effect: +0.50 × 1 = +0.50. Theta: −0.06. Vega: 0.08 × (−20) = −1.60.
- Net ≈ +0.50 − 0.06 − 1.60 = −1.16 → premium ≈ 1.84.
- The stock went up, yet the call lost about $116 per contract.
Direction is only one of several forces on an option's price.
Common misconceptions
“Delta is the probability of expiring in the money.”
It is sometimes used as a rough proxy, but it is a price sensitivity, not a probability.
“High IV means the stock will go up.”
IV reflects expected magnitude of movement, in either direction.
Checkpoint