I've been curious why vanilla options are quoted (and traded) in terms of volatility. Considering that every financial institution has its own options pricing model, volatility as an input would cause different prices for the same option. It would be obvious if the contracts were standardized and the models were explicitly specified. This, however, is not the case because the FX products are quoted in the same way, and the FX markets are OTCs.

Could someone shed some light on this?

Thanks