If I use FinancialDerivative for the American-style put option with no method chosen, but a diagonal choice "GridSize"->{npts,npts}, the method apparently converges as npts increases. My questions:

Q1. With this diagonal choice, can I rely on the convergence being to the correct value?

Q2. I need 7 good digits and, if the answer to Q1 is 'yes', apparently npts = 640,000 suffices for my parameter set. Is there a rule of thumb for how large npts needs to be for d good digits? That is, what is the order of convergence (for the American-style put)?

Q3. Is there any better/recommended relationship between the two values in "GridSize"->{npts1,npts2} for achieving efficient convergence?

Q4. What is going on "under the covers"? The documentation is, for Mathematica, unusually poor on that.