[Quantlib-dev] FD American Options Pricing

[Kyle K. <kk...@st...>]

Hi,

I'm trying to understand how the finite-differences American Options 
pricing in QuantLib works.  Specifically, I've been looking into the 
FDDivdendAmericanEngine class but am having a bit of trouble 
understanding the algorithm on a high level because of the multiple 
levels of inheritance.  As I understand it, it implements a Crank 
-Nicolson fully centered finite difference method by iterating backwards 
in time over a grid of prices, but please correct me if I'm wrong.  Note 
that I've just been running this class as it's used in the 
quanlib-benchmark program.

My main questions involve how the dimensions of the grid are determined:

- How are the number of price levels determined?  (They seem to be fixed 
at 100 in the benchmark).
- How are the time-steps of the grid determined?  Mu understanding is 
that these methods typically use constant time steps, but the quantlib 
implementation seems to vary them.  I determined this by looking in 
rollbackImpl() found in finitedifferencemodel.hpp.  I don't fully 
understand why rollback() gets called multiple times with a subset of 
the steps as opposed to calling it once with all steps.

I couldn't find any documentation that describes the algorithms used in 
QuantLib, but if it exists please point me to it.  Any help you can 
provide me in terms of understanding the high-level or my specific 
implementation questions would be greatly appreciated.  Thanks in advance,

Kyle