Finite difference method

[idorrington92]

This PR adds a finite difference method for option pricing.

• It is mostly based on the kBlack::fd_runner method here https://github.com/domokane/CompFin/blob/main/Week%204/xladdin/Utility/kBlack.cpp
  Main differences are that I've tried to decouple some of the methods (in particular, updating the finite difference matrix and rolling backwards/forwards are now handled separately) and I didn't make my code object oriented
• Tests compare the output of this model to those in the C++ code linked above, as well as to other models in FinancePy. I've left in the comparisons between different models, but it might be better to just compare to a value if we trust the finite difference model now (the models only agree to 1dp, not sure how similar we expect them to be)
• I think I've put things in logical places in the code, but happy to move things around
• I used numba where it sped up the code, but don't have too much experience with it so it could maybe have been done better
• I'm new to finance, so sorry if any comments/function names/variable names have used the wrong terminology!

[domokane]

Hi Iain
Good work ! I will look over it in the next few days.
Best
D

[domokane]

Hi Iain
Great start. It now needs to be wired into the equity vanilla option product as a new Black Scholes model implementation. This is especially useful for valuing an Equity American Call and Put option - it is a useful test but not so interesting for the European option as this has a closed form solution. It would be good to compare the finite difference approach to the CIR tree.
Best
D

[luciferbenz826]

Great work on adding the finite difference method for option pricing! Decoupling methods and handling matrix updates separately is a smart approach. The comparisons with C++ code and other models in Singapore GST provide a solid validation. Your efforts are appreciated, and the logical organization of the code is a plus. Looking forward to more contributions.