This is part of option Greeks tutorials. See also delta, gamma, theta, rho.

## What Is Vega

Options generally benefit from rising volatility, although some options more than others. Vega measures an option's sensitivity to volatility – by how many dollars the option premium will change if implied volatility increases by one percentage point *and other things remain the same*.

Unlike delta, gamma, theta, or rho, *vega* is not really a Greek letter. Some resources prefer to call it kappa.

## Why Is It Called Vega?

It is unclear who was the first to start using *vega* as the name for an option's sensitivity to volatility, and when (it has certainly been known and used in 1980's).

It is also unclear *why* the name *vega* was chosen. Two most likely reasons are:

- It starts with
**v**– like theta starts with**t**(time) or rho starts with**r**(rate). - It kind of sounds Greek (or at least scientific).

Unfortunately, there is no letter **V** in the Greek alphabet. If there was one, it would most likely be used for this Greek.

## Option Vega Symbol

Because there is no Greek letter **V**, the symbol used for option vega is either the latin **v** or the symbol for Greek letter *nu*, which looks very similar: **ν**.

## Option Vega Example

Consider a call option on a stock (the strike and underlying price are not important in this example). The option currently trades at $2.49 (option premium) and its vega is 0.13. Its implied volatility is 18%, which means the market expects volatility of the underlying stock's price to be 18% during the period from now to the option's expiration.

Market's expectations about future volatility can change for a variety of reasons (e.g. approaching company earnings, industry events, or changing perceptions of the general economy). In general, investors expect higher volatility when they are more uncertain about the future, and vice versa. Note that more uncertain doesn't always mean more pessimistic. Volatility works both ways; it is not about direction, but about size of potential price moves.

In our example, if the market becomes more uncertain about the stock's future and implied volatility rises by one percentage point from 18% to 19%, our call option's price increases by 0.13 (the vega) from $2.49 to $2.62. This assumes everything else remains the same. If the changed expectations also cause the underlying stock price to move, the option's price change will also reflect that and may be different from $2.62.

## Vega Units

Vega is a ratio of price change (in dollars) to volatility change (in percentage points). Therefore, its units are dollars per percentage point. That said, in practice the units are rarely mentioned, as with the other Greeks.

## Vega Values

All options become more valuable when volatility rises. Therefore, **vega is positive for both calls and puts.**

There is no theoretical upper limit on the values vega can reach.

Of the two components of option premium, volatility (and vega) only affects time value; it has no effect on intrinsic value. Therefore, as a rule of thumb, options with more time value have higher vega.

Vega is negative for all short option positions. Positions in the underlying security have zero vega.

## Vega and Option Moneyness

**At the money options have greatest time value and highest vega.** Options further away from the money to either side (in the money, out of the money) have less time value and lower vega.

While at the money options have greatest vega in absolute terms, out of the money options have greatest vega as percentage of their total (intrinsic + time) value, as their premium consists of time value only. Longer term out of the money options can be good vehicles for speculating on volatility (high vega for relatively low cost), with relatively small exposure to direction (delta and gamma).

## Vega and Time to Expiration

Longer dated options are more sensitive to volatility, because over a longer time period, volatility has more time to act in the option holder's favor. **The more time to expiration, the higher vega.** As an option approaches expiration and loses time value, its vega goes down.

## Vega and Volatility

When implied volatility changes, vega itself can change. Not so much for at the money options – their vega is relatively stable over a wide range of volatility levels.

Options deeper in the money or further out of the money can have very low vega when implied volatility is low (and their time value is near zero). As volatility rises, their vega gradually increases, although it never exceeds the vega of at the money options with the same expiration and underlying.

In other words, when volatility is high, the differences in vega across a wide range of strikes are quite small (although at the money strikes still have highest vega). When volatility declines, the differences become much bigger, mainly due to far out of the money and deep in the money strikes' vega falling, while at the money vega stays more or less the same.

## How to Calculate Vega

Mathematically, vega is the derivative of option premium with respect to volatility. Like the other Greeks tutorials, this tutorial focuses mainly on the logic and practical considerations, and those interested in the exact formulas can find them in Black-Scholes Greeks Formulas and Option Greeks Excel Formulas.

## Summary

- Vega measures how option price will change if implied volatility rises by one percentage point.
- All options have positive vega – gain value with rising volatility.
- Vega is greatest at the money (but out of the money in percentage terms).
- The more time to expiration, the higher vega.