Vega is one of the most important Greeks, but it often doesn't get the respect it deserves. Vega is the amount a theoretical option's price will change for a corresponding one-unit (percentage-point) change in the implied volatility of the option contract. Simply stated, Vega is the Greek that follows implied volatility (IV) swings.
Don't forget we're talking about implied volatility (IV) here, not historical volatility. Implied volatility is calculated from the current price of the option using a pricing model (Black-Scholes, Cox-Ross-Rubinstein, etc.); it's what the current market prices are implying future volatility for the stock to be.Just like the Greeks, implied volatility is determined by using a pricing model. Likewise, there is a marketplace expectation of how the option's price might change due to this parameter. But as before, there is no guarantee that this forecast will be correct.
Historical volatility is calculated from actual past price movements in the underlying security. Historical volatility may also be referred to as stock volatility or statistical volatility.
Let's consider an example: a 100 strike call option, with the stock trading at $100, 30 days to expiration, and implied volatility of 20%. The price of the option is $2.50 and the vega is equal to .115 or 11.5 cents. This means if nothing else in the marketplace changes except the option's IV increases one percentage-point from 20% to 21%, this contract would trade for around $2.50 + .115, or $2.615. If volatility declines by one percentage-point (20% to 19%), you'd expect the option price to decline in the same fashion – by the amount of the vega.
Which options tend to have large vega?
Vega is typically larger for options in the far-term, which have more time premium. It's also usually larger for at-the-money (ATM) options versus in- or out-of-the-money contracts. Think of it in these terms: the further out you go in time, the larger the amount of time premium in an option's price. More time until expiration means the contract is more susceptible to IV fluctuations.
Like gamma, vega is positive when you buy options and negative when you sell them. The sign is not affected whether trading a call or put.
Vega is also usually higher for option contracts that trade with higher implied volatilities, since higher volatility typically drives up the cost of the option. More expensive underlyings also translate to large vega. Options that meet either of these criteria are typically more sensitive to changes in implied volatility.
Vega: a tale of two stocks
To give you a feel for what this all means, let's look at two very different (and fictitious) companies _ High Flyer Tech, Ltd. and Stable Manufacturing Inc. High Flyer has all the characteristics mentioned above. It's a higher-priced stock ($390), and has a higher implied volatility (33%) when compared to Stable ($75 and 17% respectively). To show you how vega levels are sensitive to all the factors mentioned above, we chose calls with expiration dates further in the future for High Flyer than for Stable (56 days versus 28 days until expiration).
First, let's compare High Flyer's ATM strike price, 390, to the in- and out-of-the-money strikes. As expected, vega is much larger for the 390 strike: 0.61 or 61 cents. This means if the implied volatility of this option moves one percentage-point up or down, the option value would either increase or decrease by 61 cents. It's worth noting the vega for the out-of-the-money 440 strike is smaller, but it represents a larger percentage of the option's premium. It is 44 cents of $5.50 (8.0%) compared to 61 cents of $22.10 (2.7%).
Now let's turn to Stable's calls with 28 days until expiration. Stable's stock is trading at a much lower per-share price compared to High Flyer and with lower implied volatility. Here we're looking at relatively nearer-term options. The vega for the ATM strike is .08 or 8 cents – much smaller than High Flyer's ATM call at 61 cents.
At the same time, on a percentage basis, eight cents is still a major factor in the price; eight cents of $1.45 equals 5.5% of the option's price. So if this contract's IV moves just one percentage-point lower, this option will lose 5.5% of its value. Decreasing implied volatility is one of the most annoying occurrences for option buyers: sometimes you're right about the direction, but you still lose on the trade because of a drop in IV, also known as an implied volatility crunch.