In section 7 we covered implied volatility. We also covered how implied volatility often varies across different strikes and expirations.
Implied volatility will vary over time as the market’s view on future volatility changes, sometimes triggered by underlying price movements. It can be very useful then to know how option prices will react to changes in IV. This is what vega tells us.
Vega definition
Vega is a measure of the option price’s sensitivity to changes in implied volatility. More specifically, it tells us how much the option price will change with a 1% increase in IV.
Vega is always positive for option buyers, meaning their option will gain value if implied volatility increases. Implied volatility is that figure for volatility, which when entered into the black scholes option pricing model, will give the option price as the output. This means that all other things being equal, a higher IV means a higher option price, by definition. You could also say that option buyers are long volatility, as an increase in volatility will lead to an increase in their option’s value, and a decrease in volatility will lead to a decrease in their option’s value.
For option sellers, their vega is negative. As we just covered, an increase in IV will mean an increase in the value of the option, but for the seller of the option, this represents a loss. Similarly a decrease in IV will lead to a decrease in the value of the option, which for the seller of the option represents a profit. Option sellers therefore are short volatility.
This is true for both puts and calls, so:
The buyer of a call option has a positive vega.
The buyer of a put option also has a positive vega.
The seller of a call option has a negative vega.
The seller of a put option also has a negative vega.
Of course, any gain for the option buyer is a loss for the option seller, and vice versa.
For example:
An option with a vega of 20 will gain $20 of value if implied volatility increases by 1%. This would represent a $20 increase in profit for the buyer of the option, and a $20 decrease in profit for the seller of the option.
An option with a vega of 0.35 will gain $0.35 of value if implied volatility increases by 1%. This would represent a $0.35 increase in profit for the buyer of the option, and a $0.35 decrease in profit for the seller of the option.
Vega is stated as a dollar amount, i.e. the amount of dollars the option price is expected to increase by if IV increases by 1%, assuming all else remains constant. Even on the Deribit platform, where the option premiums are paid and received in amounts of cryptocurrency, the Greeks (including vega) are quoted in their dollar amounts, as calculated by the black scholes option pricing model.
Summary
An option’s vega tells you how much the option price will change in dollars if IV increases by 1%. This is assuming that everything else, like the underlying price and time to expiry, remains the same.
Option buyers have positive vega, meaning they will gain value when IV increases, and lose value when IV decreases. They are long volatility.
Option sellers have negative vega, meaning they will lose value when IV increases, and gain value when IV decreases. They are short volatility.
Vega is not static over the life of the option. While vega is the sensitivity of the option price to IV, vega itself has sensitivity to various parameters. We will cover these throughout the rest of section 10.