I am very new to finance, so I don't know if my question makes sense but I have seen that there are different methods to estimate the implied volatility of an American Option.
One of them is the finite differences method (used in the RQuantlib package in R), but since it is a mathematical method, what financial theory can it be used with to get the implied volatility ? Is it based on the Black and Scholes model ? Also is there any article or book I could read to better understand ?
Thank you in advance