# The relationship between vega and implied volatility

By Simon Gleadall, CEO of Volcube.

There is often a great deal of confusion amongst people learning to trade options about how vega and implied volatility are related. This is understandable when traders seem to inter-change between saying they are ‘long vega’ and ‘long implied volatility’ or just ‘long vol’. So what is the connection between vega and implied volatility?

It is quite simple to understand the difference. First, take some basic definitions of the two terms. Implied volatility is the *expected* volatility in the product underlying the options, given the $ price of the options. Vega is the change in an option’s value for a change in implied volatility. Now let’s translate these definitions into something more readily understood.

Think of implied volatility as another way of saying ‘the price of options’. If John own options, John would like to see their price increase, so John is in effect ‘long implied volatility’. John wants to see implied volatility increase.

Now think of vega as the* sensitivity* of options to the value of implied volatility. All options have positive vega, which means if you own options, you own vega. When you think of implied volatility as the *price* of options, you can see that options must be more valuable if the implied volatility rises; and given that vega tells us how option values change if the implied volatility changes, clearly options have positive vega. Therefore, if John owns options, he is long vega. This means his portfolio of options is *positively* sensitive to the value of implied volatility. In other words, if implied volatility increases, John’s portfolio will make a profit*. *

So vega and implied volatility are definitely not the same thing but they are related. Vega tells us an option’s (or an option portfolio’s) sensitivity to implied volatility. Whereas implied volatility can be viewed as the price of options. But if you have say a long option position, you will be long vega *and* long implied volatility. You can make money in this situation from rising implied volatility *because* options have positive vega.

*“I am long implied volatility right now.” *

* *Translation: The trader owns some options and will profit from a rise in implied volatility.

*“I am short vega and hoping vol will fall.” *

Translation: The trader is short options. If implied volatility falls, the options he is short will fall in value and he will therefore profit.

*“I’m short vol right now. I’d like to cover this by buying some vega.”*

Translation: The trader is short options. He wants to buy some options back to cover his exposure to implied volatility rising.

*“Vega is really cheap right now.”*

Translation: Really the trader means implied volatility is cheap. Vega does not have a price as such. What he says would be understood by everyone else in the market, but technically is perhaps not 100% valid.

So you can see that vega and implied volatility are often used inter-changeably but there meanings are not identical. The most important thing is to understand the difference between the two. Implied volatility reflects the value of options. Vega reflects the sensitivity of option value to implied volatility. But as we have seen many meaningful sentences can be formed using both words seamlessly.

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