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It’s a bit of a weird concept.

So, first of all, you have an underlying asset (say, a share in a company, or a barrel of oil) whose price bounces around in an unpredictable way. People like to trade these, but for various reasons people also like to trade “derivatives” which are built on top of an underlying asset.

A simple example of a derivative is a “European call option”. This is a contract which gives the holder the right to buy an underlying asset, for a specified price, on a specified date. Suppose there is a share worth $10. Suppose you buy an option from me which allows you to buy one of these shares from me for $10 in 1 month time. You pay me $1 for this option. If the stock is trading at $15 next month, you can buy it from me for $10, immediately sell it for $15, and you have made $4 in profit. On the other hand, if the stock is trading at $8 next month, the option is worthless and you have simply wasted $1.

So the value of the option depends purely on the future value of the underlying asset. And if we think we understand how the underlying asset behaves, we can work out how much the option “should” be worth. There are various mathematical models you can use to do this, the most well known being the Black-Scholes model. It turns out that the main factor that influences the value of an option is the volatility of the underlying asset – that is, how much its price tends to jump around. You can use these models to calculate the appropriate price of an option given the volatility of the underlying asset, or alternatively you can turn it around, and ask what the volatility of the underlying should be, given the current price of the option. This is the “implied volatility”.

Caveats: all of these models involve simplifications, so none of them really work perfectly. And in finance you have the weird problem that the models themselves affect real-world prices: if someone comes up with a shiny new model and everyone thinks it’s amazing and starts using it, then this will change how they trade. And of course the volatility of the underlying isn’t *really* the only factor that influences the price of the option.