A bit of a preview of some topics
Several chapters are devoted to FDM for 2-factor European/American options We tested the relatrve performance on spread options for the same level of accuracy:
1 Saulyev ADE : 1 second
2 Barakat and Clark 2.2
3 Yanenko 4.2
4 "Classic" ADI 4.0 (4 times slower!)
5 Predictor-Corrector 3.8
6 Marchuk-Strang 7.6
. Methods 1+2 do not involve solving matrix systems. 3-6 solve tridiagonal systems.
. It is possible to compute greeks by writing them as PDEs and using CSE approach (essentially tbe Cauchy-Kowalewski (Lax-Wendroff) technique). We did it for 1-factor and CSE for spreads should also be fast as well.
. Sauly'ev ADE is also the easiest to program.
. We mapped PDEs to unit square making boundary conditions easy (Fichera theory).
. Schemes 1 and 2 can easily be applied to 3-factor problems.,
. Code used is C++20, of course.
. The methods are also applicable to fixed income (Hull-White, CIR-style, mean-reverting).