# Implied volatility as price transform

1. Implied volatility

The way I understand it, traders often think of implied volatility as a transformed price. So in a way, the Black Scholes model is considered a 'model-free' blackbox that takes a market price and returns an 'implied volatility'. A trader might very well say 'I bought AstraZeneca at 20 vol'. Why is that they prefer implied vol as a price?

1. Implied vol surface

When you devise a new stochastic volatility model, you want it to match the empirical volatility surface as closely as possible (thereby matching the price surface as closely as possible because there is this one to one relationship between implied volatility and price). Why do quants prefer the implied vol surface instead of bespoke price surface?

Thanks!

• Isn't it because it's just more intuitive to speak about volatility of the underlying asset instead of the price of the option? With the volatility you can directly see things like : "The implied vol of Stock A at 3 months is $x\%$", which means that the market expect a $x\%$ vol over a 3 months period. It would have been much less intuitive if I say to you that the price of the 3 months option is $p$. – Louis. B Nov 24 '15 at 23:34
• You wrote "Black Scholes model is considered a 'model-free' blackbox". Blackbox yes, but certainly not model-free. – noob2 Nov 25 '15 at 17:07