boundary condition question.
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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 ------------------------------------------------------------------------- This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the world http://moblin-contest.org/redirect.php?banner_id=100&url=/ _______________________________________________ QuantLib-users mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-users |
Re: boundary condition question.
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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]>
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Re: boundary condition question.
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On Mon, 2008-10-20 at 21:01 +0200, jean-marc mercier wrote:
> 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. True, they both work. When you're deep in the money the delta is close to 1 and the value is close to S; deep out of the money the value and the delta are both close to 0. Luigi -- The surest way to make a monkey of a man is to quote him. -- Robert Benchley ------------------------------------------------------------------------- This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the world http://moblin-contest.org/redirect.php?banner_id=100&url=/ _______________________________________________ QuantLib-users mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-users |
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In reply to this post by jean-marc mercier
One of the best places to see how BCs have been solved is www.wilmott.com, especially Numerical Methods.
The situation is very, very extensive.
Daniel Duffy 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]>
------------------------------------------------------------------------- This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the world http://moblin-contest.org/redirect.php?banner_id=100&url=/ _______________________________________________ QuantLib-users mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-users |
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In reply to this post by jean-marc mercier
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
// You need to install Texpoint to view the maths formulae
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]>
------------------------------------------------------------------------- This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the world http://moblin-contest.org/redirect.php?banner_id=100&url=/ _______________________________________________ QuantLib-users mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-users |
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