# Implied volatility and greeks for american option with discrete dividends

What methods are available to calculate IV and greeks for an american option with discrete dividends, and how do they compare?

Should I use Roll-Geske-Whaley and solve for a given option price?

Basically, you set up a finite grid of potential stock prices $S_{n,t}$ and corresponding options values $V_{n,t}$, where $V$ starts out unknown. You know what $V$ looks like at the option expiration time $T$, and so you fill that in and then work backwards from $T$, filling in $V$ values as you go.
The American exercise comes in when you figure out for which cases $V_{n,t}$ would be bigger by exercising early.