solving n euqations with n unknowns

[Adjriou Belak]

Hi,

 

I would like to implement a method with cubic interpolation for an an interest curve so I need to get

a newton Raphson algorithm to do that.

 

Do you know if there is this algorithm in quantlib or a solver wich takes my equations and my unknowns ?

 

regards,

belak

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[Adjriou Belak]

Hi Ashish,

thanks for your answer,

 

I'm trying to solve non linear equations. Actually I want to find zero rates  which fit bond Prices but I would like to smooth the curve by making a cubic interpolation. So I can't bootstrap because the current bond needs the next bond with a maturity higher than itself.

 

Thanks a lot.

I would like to integrate Newton-raphson algorithm to quantlib.

 

 

 

Ashish Kulkarni <[hidden email]> wrote:

AFAIK QuantLib doesn't have a N-dimensional solver. Building such a 
solver is a non-trivial task, to say the least  :-)

Section 9.6 and 9.7 of "Numerical Recipes in C" has very good and highly 
technical discussions regarding the problem (and some implementations, too).

http://www.library.cornell.edu/nr/bookcpdf.html

GSL has quite a few N-dimensional solvers also but it's GPL, so it might 
or might not fit your requirements.

http://www.gnu.org/software/gsl/manual/gsl-ref_34.html

Hope this helps,
Ashish

------------------------------------------------------------------------
Honest disagreement is often a good sign of progress.
     -- Gandhi


> Hi,
>  
> I would like to implement a method with cubic interpolation for an an 
> interest curve so I need to get
> a newton Raphson algorithm to do that.
>  
> Do you know if there is this algorithm in quantlib or a solver wich 
> takes my equations and my unknowns ?
>  
> regards,
> belak

Greetings!

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[Ashish Kulkarni-6]

AFAIK QuantLib doesn't have a N-dimensional solver. Building such a 
solver is a non-trivial task, to say the least  :-)

Section 9.6 and 9.7 of "Numerical Recipes in C" has very good and highly 
technical discussions regarding the problem (and some implementations, too).

http://www.library.cornell.edu/nr/bookcpdf.html

GSL has quite a few N-dimensional solvers also but it's GPL, so it might 
or might not fit your requirements.

http://www.gnu.org/software/gsl/manual/gsl-ref_34.html

Hope this helps,
Ashish

------------------------------------------------------------------------
Honest disagreement is often a good sign of progress.
     -- Gandhi


> Hi,
>  
> I would like to implement a method with cubic interpolation for an an 
> interest curve so I need to get
> a newton Raphson algorithm to do that.
>  
> Do you know if there is this algorithm in quantlib or a solver wich 
> takes my equations and my unknowns ?
>  
> regards,
> belak

Greetings!

ICICI Infotech is now 3i Infotech.

The e-mail addresses of the company's employees have been changed to <existing name>@3i-infotech.com. You are requested to take note of this new e-mail ID and make use of the same in future

"This e-mail message may contain confidential, proprietary or legally privileged information. It should not be used by anyone who is not the original intended recipient. If you have erroneously received this message, please delete it immediately and notify the sender. The recipient acknowledges that 3i Infotech or its subsidiaries and associated companies, (collectively "3i Infotech"), are unable to exercise control or ensure or guarantee the integrity of/over the contents of the information contained in e-mail transmissions and further acknowledges that any views expressed in this message are those of the individual sender and no binding nature of the message shall be implied or assumed unless the sender does so expressly with due authority of 3i Infotech. Before opening any attachments please check them for viruses and defects."

[Aurelien Chanudet-2]

Hi,

I have myself implemented a BSpline interpolated term
structure class but haven't yet contributed the code
back because none of QuantLib numerical constrained
optimisation methods seem to achieve satisfactory
results in a reasonnable time (although Excel's solver
does). When time permits, I'm planning to enhanced the
built-in optimisation method. Any feedback or pointers
on this is appreciated.

Aurelien

> Hi,
>  
> I would like to implement a method with cubic
> interpolation for an an interest curve so I need to
> get
> a newton Raphson algorithm to do that.
>  
> Do you know if there is this algorithm in quantlib
> or a solver wich takes my equations and my unknowns
> ?
>  
> regards,
> belak

       

       
               
__________________________________________________________________
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[Aurelien Chanudet-2]

Thanks for the hint. I've already tried "Numerical
Recipes in C". Most of the algorithms I tested
converges but, to my understanding, only constrained
free problems are tackled here. What I'm interested in
is constrained minimization. By the way, what I'm
trying to implement is described in :

Interest Rate Modelling
Jessica James and Nick Webber
Wiley
p. 436

(A good reference, despite numerous typos.)

> IIRC splines are basically polynomials, thus an
> optimization (or more
> correctly, root-finding) algorithm designed
> specifically for polynomials
> would probably be better. "Numerical Recipes in C"
> is your friend --
> chapters 9 and 10 are very good.
>
> Wish you luck  :-)
>
>

------------------------------------------------------------------------

> For every problem there is a solution which is
> simple, clean and wrong.
>      -- Henry Louis Mencken
>
> Aurelien Chanudet wrote:
>
> > Hi,
> >
> > I have myself implemented a BSpline interpolated
> term
> > structure class but haven't yet contributed the
> code
> > back because none of QuantLib numerical
> constrained
> > optimisation methods seem to achieve satisfactory
> > results in a reasonnable time (although Excel's
> solver
> > does). When time permits, I'm planning to enhanced
> the
> > built-in optimisation method. Any feedback or
> pointers
> > on this is appreciated.
> >
> > Aurelien
> >
> >
> >>Hi,
> >>
> >>I would like to implement a method with cubic
> >>interpolation for an an interest curve so I need
> to
> >>get
> >>a newton Raphson algorithm to do that.
> >>
> >>Do you know if there is this algorithm in quantlib
> >>or a solver wich takes my equations and my
> unknowns
> >>?
> >>
> >>regards,
> >>belak
>
> --
> Greetings!
>
>  
>
>
> ICICI Infotech is now 3i Infotech.
>
>
> The e-mail addresses of the company's employees have
> been changed to <existing name>@3i-infotech.com. You
> are requested to take note of this new e-mail ID and
> make use of the same in future
>
>  
> "This e-mail message may contain confidential,
> proprietary or legally privileged information. It
> should not be used by anyone who is not the original
> intended recipient. If you have erroneously received
> this message, please delete it immediately and
> notify the sender. The recipient acknowledges that
> 3i Infotech or its subsidiaries and associated
> companies, (collectively "3i Infotech"), are unable
> to exercise control or ensure or guarantee the
> integrity of/over the contents of the information
> contained in e-mail transmissions and further
> acknowledges that any views expressed in this
> message are those of the individual sender and no
> binding nature of the message shall be implied or
> assumed unless the sender does so expressly with due
> authority of 3i Infotech. Before opening any
> attachments please check them for viruses and
> defects."
>
>

       

       
               
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[Ashish Kulkarni-6]

hello Adjriou,

can't help you directly, but I'd suggest looking at these great articles:

The Art and Science of Curve Building
http://www.fincad.com/news/jun04/The%20Art%20of%20Curve%20Building.pdf

David Cox: Yield Curves and how to build them
http://tinyurl.com/7y5vb

Excel/VBA of McCulloch's model
http://tinyurl.com/5dpqz

Hope this helps,
ashish

------------------------------------------------------------------------
The great use of life is to spend it for something that will outlast it.
     -- William James

Adjriou Belak wrote:
> Hi Ashish,
> thanks for your answer,
>  
> I'm trying to solve non linear equations. Actually I want to find zero 
> rates  which fit bond Prices but I would like to smooth the curve by 
> making a cubic interpolation. So I can't bootstrap because the current 
> bond needs the next bond with a maturity higher than itself.
>  
> Thanks a lot.
> I would like to integrate Newton-raphson algorithm to quantlib.

Greetings!

ICICI Infotech is now 3i Infotech.

The e-mail addresses of the company's employees have been changed to <existing name>@3i-infotech.com. You are requested to take note of this new e-mail ID and make use of the same in future

"This e-mail message may contain confidential, proprietary or legally privileged information. It should not be used by anyone who is not the original intended recipient. If you have erroneously received this message, please delete it immediately and notify the sender. The recipient acknowledges that 3i Infotech or its subsidiaries and associated companies, (collectively "3i Infotech"), are unable to exercise control or ensure or guarantee the integrity of/over the contents of the information contained in e-mail transmissions and further acknowledges that any views expressed in this message are those of the individual sender and no binding nature of the message shall be implied or assumed unless the sender does so expressly with due authority of 3i Infotech. Before opening any attachments please check them for viruses and defects."

[Ashish Kulkarni-6]

IIRC splines are basically polynomials, thus an optimization (or more 
correctly, root-finding) algorithm designed specifically for polynomials 
would probably be better. "Numerical Recipes in C" is your friend -- 
chapters 9 and 10 are very good.

Wish you luck  :-)

------------------------------------------------------------------------
For every problem there is a solution which is simple, clean and wrong.
     -- Henry Louis Mencken

Aurelien Chanudet wrote:

> Hi,
> 
> I have myself implemented a BSpline interpolated term
> structure class but haven't yet contributed the code
> back because none of QuantLib numerical constrained
> optimisation methods seem to achieve satisfactory
> results in a reasonnable time (although Excel's solver
> does). When time permits, I'm planning to enhanced the
> built-in optimisation method. Any feedback or pointers
> on this is appreciated.
> 
> Aurelien
> 
> 
>>Hi,
>> 
>>I would like to implement a method with cubic
>>interpolation for an an interest curve so I need to
>>get
>>a newton Raphson algorithm to do that.
>> 
>>Do you know if there is this algorithm in quantlib
>>or a solver wich takes my equations and my unknowns
>>?
>> 
>>regards,
>>belak

Greetings!

ICICI Infotech is now 3i Infotech.

The e-mail addresses of the company's employees have been changed to <existing name>@3i-infotech.com. You are requested to take note of this new e-mail ID and make use of the same in future

"This e-mail message may contain confidential, proprietary or legally privileged information. It should not be used by anyone who is not the original intended recipient. If you have erroneously received this message, please delete it immediately and notify the sender. The recipient acknowledges that 3i Infotech or its subsidiaries and associated companies, (collectively "3i Infotech"), are unable to exercise control or ensure or guarantee the integrity of/over the contents of the information contained in e-mail transmissions and further acknowledges that any views expressed in this message are those of the individual sender and no binding nature of the message shall be implied or assumed unless the sender does so expressly with due authority of 3i Infotech. Before opening any attachments please check them for viruses and defects."