An option's price can change with the stock unmoved and no day gone by. All it takes is the market changing its mind about how much the stock is likely to move. That expected movement, priced into the options themselves, is called implied volatility, and vega is how much each option cares about it. For anyone trading options rather than stock, vega is often the Greek that decides the result.
Sensitivity per vol point
Vega is the change in an option's price when implied volatility rises by one percentage point, for example from 30% to 31%. The chain quotes it per share. Say an AMZN call trades at $8.00 with a vega of 0.25. If the market re-prices the stock's expected movement from 30% to 32%, two points, the call rises about 50 cents to $8.50, or $50 on the contract, without AMZN moving at all. If implied volatility falls two points, the call loses the same. Vega is positive for anyone who owns an option, call or put alike, and a call and a put at the same strike carry the same vega. The seller is short vega.
Vega is the slope of each line. At the money the line is nearly straight, so vega is steady; out of the money it bends upward, so vega grows as volatility rises.
Vega grows with time to expiration
An at-the-money option's price grows roughly with implied volatility times the square root of the time left. So its vega grows with the square root of time too. Four times the days gives about twice the vega: a four-month option carries roughly double the vega of a one-month option at the same strike. Stretch it further and a one-year option carries about seven times the vega of a one-week option, because the square root of 52 is a little over 7.
Across strikes, vega in dollar terms is largest at the money and smaller in the wings, for the same reason theta and gamma are: the at-the-money option holds the most time value, and time value is the part that implied volatility prices.
Per-share vega of the same strike with a year, three months, a month and a week left. Four times the days gives about twice the vega.
Vol trades and gamma trades
Put the last three lessons side by side and a split appears.
- A short-dated at-the-money option has large gamma, large theta and small vega. Its result over the next few days depends on how much the stock actually moves against the decay paid. That is a gamma trade: a bet on realized movement.
- A long-dated at-the-money option has small gamma, small theta and large vega. A $2 move in the stock barely registers, but a two-point change in implied volatility does. That is a vol trade: a bet on the market's expectation changing.
Both are bought the same way, with a call or a put, which is why beginners get caught. Buy a six-month straddle ahead of a news event and the stock can jump exactly as you hoped while the position loses, because implied volatility fell once the news was out and vega swamped gamma. Match the expiration to the bet you actually want to make.
The maths: vega and the square root of time
Vega is S e^(-qT) n(d1) √T per unit of volatility, which the chain divides by 100 to quote per vol point. At the money, n(d1) is about 0.4, so vega is roughly 0.4 × S × √T / 100. For a $100 stock that is about 0.40 with a year left and about 0.055 with a week left, a ratio of a little over 7, the square root of 52.
The same approximation gives a handy rule for the price itself: an at-the-money option is worth about 0.4 × S × v × √T. Price is nearly a straight line in volatility at the money, which is why the at-the-money line in the first chart is straight and its vega barely changes as volatility moves. The out-of-the-money lines bend upward; that bend is vomma, covered later in this module.
Your turn
Open the AMZN chain. Read the at-the-money vega on the nearest expiration, then on a later monthly and compare. Then add the call and put vegas on the monthly to get the vega of a straddle.