FDM Framework and Convertible Bond

[John Maiden]

I am interested in trying to adapt the convertible bond model by
Ayache, Forsyth, and Vetzal (The Valuation of Convertible Bonds
with Credit Risk) into the FDM framework, but I'm not sure how to
do it. Specifically, I'm looking at using the PDE in eqn 4.6
from their paper.  My problem is incorporating the final term,
which depends on a function of the stock price.

In terms of the FDM framework, there are three functions I
need to define - drift, diffusion, and evolve. Drift and
diffusion I can see from the PDE. Would I add this final
term in the evolve function? In general, how could I
incorporate a PDE that has a f(S) term, where f is
non-linear?


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[Smith, Dale (Norcross)]

Take a look at

http://www.cs.toronto.edu/pub/reports/na/lucy-05-msc.pdf

This implementation discussion may help.

Thanks,
Dale Smith, Ph.D.
Senior Financial Quantitative Analyst
Risk & Compliance
Fiserv.
107 Technology Park
Norcross, GA 30092
Direct NYC: 212-419-3242
Direct Norcross: 678-375-5315
Mobile: [phone]
Mail: [hidden email]
www.fiserv.com

-----Original Message-----
From: John Maiden [mailto:[hidden email]]
Sent: Monday, May 09, 2011 11:24 PM
To: [hidden email]
Subject: [Quantlib-users] FDM Framework and Convertible Bond

I am interested in trying to adapt the convertible bond model by
Ayache, Forsyth, and Vetzal (The Valuation of Convertible Bonds
with Credit Risk) into the FDM framework, but I'm not sure how to
do it. Specifically, I'm looking at using the PDE in eqn 4.6
from their paper.  My problem is incorporating the final term,
which depends on a function of the stock price.

In terms of the FDM framework, there are three functions I
need to define - drift, diffusion, and evolve. Drift and
diffusion I can see from the PDE. Would I add this final
term in the evolve function? In general, how could I
incorporate a PDE that has a f(S) term, where f is
non-linear?


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What every C/C++ and Fortran developer should know.
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[John Maiden]

Thank you for the reference, I am familiar with the paper.

I get the general idea, my question is specifically where in the FDM framework I
would incorporate this non-linear term. I assume it would go into the evolve
function, where I would just add in this final term.


------------------------------------------------------------------------------
Achieve unprecedented app performance and reliability
What every C/C++ and Fortran developer should know.
Learn how Intel has extended the reach of its next-generation tools
to help boost performance applications - inlcuding clusters.
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[Smith, Dale (Norcross)]

After reading the design documents and looking at the tutorials as well
as the code over the past month, I would say the most appropriate place
is in evolve.

Thanks,
Dale Smith, Ph.D.
Senior Financial Quantitative Analyst
Risk & Compliance
Fiserv.
107 Technology Park
Norcross, GA 30092
Direct NYC: 212-419-3242
Direct Norcross: 678-375-5315
Mobile: [phone]
Mail: [hidden email]
www.fiserv.com


-----Original Message-----
From: John Maiden [mailto:[hidden email]]
Sent: Tuesday, May 10, 2011 8:32 AM
To: [hidden email]
Subject: Re: [Quantlib-users] FDM Framework and Convertible Bond

Thank you for the reference, I am familiar with the paper.

I get the general idea, my question is specifically where in the FDM
framework I
would incorporate this non-linear term. I assume it would go into the
evolve
function, where I would just add in this final term.


------------------------------------------------------------------------
------
Achieve unprecedented app performance and reliability
What every C/C++ and Fortran developer should know.
Learn how Intel has extended the reach of its next-generation tools
to help boost performance applications - inlcuding clusters.
http://p.sf.net/sfu/intel-dev2devmay
_______________________________________________
QuantLib-users mailing list
[hidden email]
https://lists.sourceforge.net/lists/listinfo/quantlib-users

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Achieve unprecedented app performance and reliability
What every C/C++ and Fortran developer should know.
Learn how Intel has extended the reach of its next-generation tools
to help boost performance applications - inlcuding clusters.
http://p.sf.net/sfu/intel-dev2devmay
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