Greeks: Vega | theskew

GREEKS - VEGA: Volatility impact on option premiums.

The dollar value impact on a Portfolio of a change in volatility is referred to as “Vega”.

Vega is usually measured as the expected change in the value of a Portfolio for a 1% change in volatility. It is also usually expressed as an actual dollar number.

The examples below calculate the impact on option premiums of a change in Volatility. Once the impact is calculated, the change in option premiums is scaled to a 1% change in Volatility to calculate the Vega of each premium.

We compare two scenarios where the only difference in Expected Future Stock Prices is their dispersion.

Note how everything else equal, a higher dispersion (e.g. Volatility) with the same Stock price increases the premiums of both Put and Call options.

CALCULATING VEGA:

The Examples above calculate the prices of a Call and a Put at a different Volatility.

In the High Volatility scenario the average up or down move is $30, and the average premium is $15.

In the Low Volatility scenario the average up or down move is $15, and the average premium is $7.5.

Since in both cases the initial Stock Price is 100, the High Volatility scenario corresponds to a 30% Volatility; The Low Volatility scenario corresponds to a 15% Volatility.

For the options in the examples above, the results of a 15% change in volatility correspond to a $7.5 change in premium.

The examples illustrate the impact of volatility on option premiums. At a higher volatility, the same options are worth more. We can also use the numbers obtained to calculate Vega, defined as the dollar impact of a 1% change in volatility.

The Examples use a 15% change of Volatility to calculate different option premiums. We can obtain Vega by dividing by 15 the change in option premiums.

The resulting Vega of each of each of the options is $0.50, the dollar impact of a 1% change in volatility. It is calculated by re-scaling from 15% to 1% the the impact in premium changes as a result of volatility changes ($7.5 change in premium divided by 15 - for 15% change in volatility from 15% to 30%).