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Quantlib Benchmark: Monte Carlo methods and Finite Difference

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jean-marc mercier

Quantlib Benchmark: Monte Carlo methods and Finite Difference

Hello,

I am trying to develop some numerical methods for pricing multi underlying exotic instruments, either European or American, using what I call "optimal schemes" techniques.

To benchmark these methods, I integrated new pricers to the QL framework, in order to compare their performances to their equivalent QL pricers. A first round of test is available at URL

http://www.crimere.com/Products/Optimal%20Schem%20Project/Investment%20Banking/Technical%20Overview_files/Optimal_Schemes_Results1D.pdf

These first tests concern only one underlying pricing, either european or american. The multi underlying case is under way, I will update in this forum as soon as possible.

Do not hesitate to contact me for further informations or questions.

Jean-Marc Mercier

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Luigi Ballabio

Re: Quantlib Benchmark: Monte Carlo methods and Finite Difference

On Wed, 2008-07-23 at 00:09 +0200, jean-marc mercier wrote:

> I am trying to develop some numerical methods for pricing multi
> underlying exotic instruments, either European or American, using what
> I call "optimal schemes" techniques.
>
> To benchmark these methods, I integrated new pricers to the QL
> framework, in order to compare their performances to their equivalent
> QL pricers. A first round of test is available at URL
>
> <a href="http://www.crimere.com/Products/Optimal%20Schem%20Project/Investment%">http://www.crimere.com/Products/Optimal%20Schem%20Project/Investment%
> 20Banking/Technical%20Overview_files/Optimal_Schemes_Results1D.pdf
>
> These first tests concern only one underlying pricing, either european
> or american. The multi underlying case is under way, I will update in
> this forum as soon as possible.

Hi Jean-Marc,
apologies for the delay. I haven't looked at the paper in much detail,
but the results do look interesting. Are you interested in contributing
the code?

Later,
Luigi

--

The doctrine of human equality reposes on this: that there is no man
really clever who has not found that he is stupid.
-- Gilbert K. Chesterson

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jean-marc mercier

Re: Quantlib Benchmark: Monte Carlo methods and Finite Difference

Hi Luigi,

Sorry for the delay too :)
It would be a pleasure to contribute to QuantLib project, if my humble research work could be of interest for this valuable project.

Some remarks concerning the american pricing :

1) Documentation: the one dimensional ideas are quite well understood and documented in a paper. Some works remains to do to write down the multidimensional paper.

2) Code and Disclaimer ! this is a prototype for a research work. It means that I did not put so much effort for clean code, optimization and integration: a lot of code integration remains to do to obtain a code as clean as the Quantilib PDE pricer, and some technical research probably too. Furthermore I do not rely on Quantlib for the multidimensional vector structures (I decided to develop my own multidimensional structures for performance and dimensionality templating purposes).

3) Strong Points of the method :
a) the boundary conditions are trivially handled in any dimensions.
b) the method can be generalized easily in higher dimensions. Most of the code used has been dimensionally templated.
c) The overall construction works fine if the underlying has a known density, as the geometric based brownian motions.

4) Weak points of the method
a) Non integrable underlyings (I mean motions that do not have explicitely known densities, as local volatilities based motions) can be included, but the numerical method proposed is not really convincing in that case. Probably some research has to be done here.
b) The multidimensional version of this method is a pricer converging at rate N^(-2/d), where d is the number of underlyings (the best known rate of convergence at my knowledge). I think however that a C(d)/N rate is reachable, but not with the technology I used here.

Would you be still interested by a code contribution, do not hesitate to contact me for further details or contacts. Would this discussion out of scope of the Quantlib users forum, please find included my professional e-mail adress : [hidden email]

Regards

jean-marc Mercier

2008/8/22 Luigi Ballabio <[hidden email]>

On Wed, 2008-07-23 at 00:09 +0200, jean-marc mercier wrote:
> I am trying to develop some numerical methods for pricing multi
> underlying exotic instruments, either European or American, using what
> I call "optimal schemes" techniques.
>
> To benchmark these methods, I integrated new pricers to the QL
> framework, in order to compare their performances to their equivalent
> QL pricers. A first round of test is available at URL
>
> <a href="http://www.crimere.com/Products/Optimal%20Schem%20Project/Investment%" target="_blank">http://www.crimere.com/Products/Optimal%20Schem%20Project/Investment%
> 20Banking/Technical%20Overview_files/Optimal_Schemes_Results1D.pdf
>
> These first tests concern only one underlying pricing, either european
> or american. The multi underlying case is under way, I will update in
> this forum as soon as possible.

Hi Jean-Marc,
apologies for the delay. I haven't looked at the paper in much detail,
but the results do look interesting. Are you interested in contributing
the code?

Later,
Luigi

--

The doctrine of human equality reposes on this: that there is no man
really clever who has not found that he is stupid.
-- Gilbert K. Chesterson

jean-marc mercier

Re: Quantlib Benchmark: Monte Carlo methods and Finite Difference

In reply to this post by Luigi Ballabio

Dear Luigi.

No you didn't :)

All this work will be reviewed by peers at the end of the month. If there is no contestation, I will release the code, probably current of December on my website.
Note : this work is linked to the wilmot thread http://www.wilmott.com/messageview.cfm?catid=34&threadid=65728

Regards

Jean-Marc

2008/10/27 Luigi Ballabio <[hidden email]>

Jean-Marc,
sorry---did I ever answer to this email?
Anyway:

On Wed, 2008-09-24 at 18:57 +0200, jean-marc mercier wrote:
> A bad point is that these pricers uses a lot of code and structures
> that are part of some kind of "PDE toolkit" library that I developed,
> and it seems really hard to separate them.
>
> To avoid useless work, would it be possible to release these pricers
> as experimental as a separate project including both libraries ?

Yes, I think that would be best.

Later,
Luigi

--

An ideal world is left as an exercise to the reader.
-- Paul Graham