Quote from panzerman:
No. The volatility input is an educated guess. Given the price of an option, the math can be worked out to solve for volatility (called implied volatility), but you can't know with absolute certainty what the volatility should be a priori to put into the pricing model.
The volatility on the underlying stock is the actual volatility, but is only a very rough correlation of what the implied volatility will turn out to be. There are data suppliers who keep historical actual volatility and historical implied volatility, but I don't names offhand.
Volatility estimation is a big deal, and lots of quants gain meaningful employment trying to compute its value so that it can be used by market makers and hedge funds etc.
