Posted by
Ferdinando M. Ametrano-3 on
Nov 15, 2005; 1:22am
URL: http://quantlib.414.s1.nabble.com/LMM-and-finite-difference-methods-tp4222p4223.html
On 11/15/05, Joseph Wang <
[hidden email]> wrote:
> Here is a silly question. Why is it that LMM methods are used only with
> Monte Carlo and not with finite difference methods.
LMM are intrinsically high-dimension. If you model the 30-year yield
curve as a strip of 6-month forward libor you have 60 factors. FD with
more than 3 factors are less efficient than MC, and very hard (almost
impossible?) to implement.
> I'm probably
> missing something very fundamental, but it seems mathematically possible
> to write a FDM engine that calculates the forward curve.
Many banks do not actually evolve 60 factors, but use factor analysis
(PCA) to reduce dimensionality and evolve just 2 or 3 main factors. It
might be possible to use FD for such a reduced version of LMM and a FD
implementation of reduced-dimension LMM would be great as it could
easily account for American exercise.
The lack of literature on this topic suggests me that a) it must be
undisclosed proprietary leading edge stuff, or that b) implementation
details (i.e. boundary conditions) must be so complex to make the
implementation unfeasible
ciao -- Nando