Vega measures an option's sensitivity to implied volatility, indicating how much the option's price will change with a one percentage point increase in volatility. All options have positive vega and gain value with rising volatility, with the highest vega occurring for at-the-money options, especially when there is more time to expiration. As options approach expiration, their vega decreases, and while volatility influences vega, at-the-money options maintain relatively stable vega across different volatility levels.

1. Lecture No 69
Option Greek
Vega
Rohan Sharma (Coach)

2. 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.
Vega is a ratio of price change (in dollars) to volatility change
(in percentage points) its units are dollars per percentage
point.

3. What is Vega ?
• Vega is the Greek that measures an option’s sensitivity to implied
volatility.
• It is the change in the option’s price for a one-point change in implied
volatility. Traders usually refer to the volatility without the decimal point.
• For example, volatility at 14% would commonly be referred to as “vol at
14.”
• Volatility should not be confused with Vega.
• Volatility is either the historical or expected bounciness of the underlying
future.
• Historical volatility is volatility in the past and is therefore known.
• Expected volatility is unknown volatility in the futures contract that feeds
into the option price as implied volatility.

4. Example - Vega
• Vega is the sensitivity of a particular option to changes in implied
volatility.
• For example, if the value of an option is 7.50, implied volatility is at 20
and the option has a Vega of .12.
• Assume that implied volatility moves from 20 to 21.5. This is a 1.5
volatility increase.
• The option price will increase by 1.5 x .12 = .18 to 7.68.
• Conversely, if volatility dropped from 20 to 18. This two-point decrease
times .12 equals .24, making the option premium 7.26.
• Vega is the highest when the underlying price is near the option’s strike
price. Vega declines as the option approaches expiration. The more time
to expiration, the more Vega in the option.

5. 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.

6. 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).

7. 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.

8. 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.

9. Conclusion
• 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.