An option's price moves for more reasons than just the stock price. The Greeks each measure the option's sensitivity to a different force — together, they describe exactly what a position is exposed to.
The previous lesson covered an option's payoff at expiration. Before expiration, its price — the premium — moves constantly, and not just because of the stock price. The Greeks are a set of measures, each named after a Greek letter, that isolate how sensitive an option's price is to one specific factor at a time.
Delta measures how much the option's price changes for a $1 move in the underlying stock — a delta of 0.60 means the option gains roughly $0.60 for every $1 the stock rises. Gamma measures how much delta itself changes as the stock moves — the "delta of delta," describing how quickly an option's directional exposure accelerates. Theta measures time decay: how much value the option loses purely from one day passing, holding everything else constant — an ever-present drag on a long option position. Vega measures sensitivity to implied volatility: how much the option's price changes if the market's expectation of future volatility shifts, even with the stock price unchanged.
Together, these four answer a single practical question: if the stock moves, if time passes, or if volatility expectations shift, what happens to this position? A trader who only watches the stock price is ignoring at least three of the four forces actually moving their option's value day to day.
A hypothetical call option position with the Greeks below. What each one is saying about the position — illustrative numbers only.
| Greek | Value | What It's Saying |
|---|---|---|
| Delta | +0.55 | Gains ~$0.55 per $1 the stock rises |
| Gamma | 0.04 | Delta itself rises ~0.04 per $1 stock move |
| Theta | -0.08 | Loses ~$0.08 of value per day, all else equal |
| Vega | +0.12 | Gains ~$0.12 if implied volatility rises 1 point |
Every day this option is held, theta quietly erodes ~$0.08 of value even if the stock doesn't move at all — a cost that only a directional stock move (via delta), an accelerating move (via gamma), or a rise in volatility expectations (via vega) can offset.
Enter a position's Greeks and a hypothetical change in the stock price, days passed, and implied volatility — see the estimated impact on the option's value.
Model: price impact ≈ (delta × stock move) + (0.5 × gamma × stock move²) + (theta × days passed) + (vega × IV change). A simplified second-order approximation, not an exact options pricing model — illustrative only.
Answer all five, then hit "Check My Answers" to see how you did. Get one wrong? No problem — the explanation will show you exactly why.
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Vega measures sensitivity to volatility expectations — the next lesson digs into what implied volatility actually is, and why it's rarely the same across every strike price.