- 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?
- 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?