Re: boundary condition question.

Posted by cuchulainn on Nov 02, 2008; 8:16pm
URL: http://quantlib.414.s1.nabble.com/boundary-condition-question-tp6831p6833.html

In the last while I have been working with another approach (my basic standpoint now is that truncation of the boundary and the impositions of ad-hoc BC on new boundaries is *not* the way to go).

New method involves mapping semi-infinite interval (0, INFINITY) to (0,1) (e..g. y = exp(cx), tahn(cx) etc.) and using Fichera theory. The maths is correct and very clear.

 

The idea is not new.

 

Numerics: I am getting excellent results.

 

Maybe this helps

 

Daniel

 

// slide show on Fichera BC

 

http://www.datasimfinancial.com/forum/viewtopic.php?t=76

 

 

// You need to install Texpoint to view the maths formulae

 

http://texpoint.necula.org/download.html

---

From: jean-marc mercier [mailto:[hidden email]]
Sent: Mon 20-10-2008 21:01
To: Sun, Xiuxin
Cc: [hidden email]
Subject: Re: [Quantlib-users] boundary condition question.

Dear Sun,

I am not part of Quantlib team, however I would say that none of your guess are correct: transparent Boundary Conditions should be used. However, if the grid is large enough, Neumann or Dirichlet are a correct alternative for a classical FD approach.
Note that there exists also FD approaches for European or American pay off that do not use any boundary conditions.

Regards,

Jean-Marc Mercier

2008/10/17 Sun, Xiuxin <[hidden email]>

HI,
In FDEuropeanEngine module, if I'm right, the boundary conditions are
set up in FDVanillaEngine::initializeBoundaryConditions. They are
NeumannBC, but as I know from the BS PDE,
we only know the option value on the upper and lower boundaries,
shouldn't they be DirichletBC ?

please help to advise.
thanks,
sun

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