Often, non-professional options traders have a lot of confusion regarding the relationship of vega and implied volatility. This becomes obvious when traders use phrases: “long vega”, “long implied volatility” or simply “long vol”. So, what is the connection between an option position vega and implied volatility?
It's easier to understand the difference between two terms. Let's first look at some basic definitions of these two terms. Implied volatility is the expected volatility of the underlying asset for a given option premium. Vega indicates a potential change in the value of an option if the implied volatility changes by 1%. Therefore, mathematically, vega is a 1-st order derivative of the option price with respect to volatility.
Now let us translate these definitions into something more understandable.
Implied volatility can also be called the “option price”, since implied volatility is the main component of the option price (its time value). If Alex bought options, Alex would like to see their price increase, so Alex actually “bought implied volatility”. Alex wants to see an increase in the volatility, which will lead to an increase in the price of options.
If the trader wants to trade delta, i.e. the price of the underlying asset, the easiest way is to buy/sell the underlying asset. There is no point in paying a premium. Option trading is about trading volatility. Implied volatility can be traded through vega and realized volatility is traded through gamma.
Vega should be understood as the sensitivity of an option price to changes in implied volatility. A long option position implies a positive vega. It means that if a trader has bought options, the vega is positive.
If we understand implied volatility as “option price”, we can see that the value of an option increases as the implied volatility increases. And vega indicates exactly what value (in monetary or percentage terms) an option's price will rise or fall if the implied volatility changes by 1%.
Thus, vega and implied volatility are certainly not the same, but they are related. Vega tells us about the sensitivity of an option (or option portfolio) to implied volatility. While implied volatility can be seen as the price of options. For example, if a trader has a long option position, therefore, the option portfolio is long vega or long vol. In this situation, the trader earns from increasing implied volatility because the option position has a positive vega.
Option trader's jargon
“I bought the volatility”.
Translation: the trader has bought options and will profit from increased implied volatility.
“I have a short vega”.
Translation: The trader sold options. If the implied volatility drops, the options will decrease in value. So he will make a profit.
“I am short volatility. I'd like to cover it by buying some vega”.
Translation: The trader sold options. He wants to buy options to partially cover a negative vega because he's afraid of increasing volatility.
“Vega is really cheap now”.
Translation: The trader assumes that the implied volatility is very low amid the current market situation.
Thus, vega and implied volatility are often used interchangeably, but their values are not identical. The most important thing is to understand the difference between them. Implied volatility reflects the value of options. Vega reflects the sensitivity of an option price to changes in implied volatility.