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Sobol's Low discrepency sequence

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Fabrice_CBA

Sobol's Low discrepency sequence

Hi all,

I'm working through the implementation of the Sobol number generator in QuantLib and I've got two questions on which I would appreciate any insight you can give me:

1) At the top of the file sobolrsg.cpp a variable called AltPrimitivePolynomials is set up. This variable seems to just re-order some of the primitive polynomials (as compared to the order in primitivepolynomials.c). Is there a theoretical reason for doing this, i.e. does it improve some property of the numbers generated? I haven't seen this step described in any of the literature I have read on the method (e.g. Jäckel's book).

2) Do you have any feel for which method for initialising the free direction integers provides the best results?

Thanks for your consideration.

Regards,
Fabrice

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Luigi Ballabio

Re: Sobol's Low discrepency sequence

On Mar 20, 2008, at 3:06 AM, Lecuyer, Fabrice wrote:

> I'm working through the implementation of the Sobol number generator
> in QuantLib and I've got two questions on which I would appreciate any
> insight you can give me:
>
> 1) At the top of the file sobolrsg.cpp a variable called
> AltPrimitivePolynomials is set up. This variable seems to just
> re-order some of the primitive polynomials (as compared to the order
> in primitivepolynomials.c). Is there a theoretical reason for doing
> this, i.e. does it improve some property of the numbers generated? I
> haven't seen this step described in any of the literature I have read
> on the method (e.g. Jäckel's book).
>
> 2) Do you have any feel for which method for initialising the free
> direction integers provides the best results?

Fabrice_CBA

Re: Sobol's Low discrepency sequence

Thanks Mark.

Could you please point me to a paper/book that explains the ordering for the polynomials used in QuantLib?

Regards,
Fabrice

-----Original Message-----
From: Luigi Ballabio [mailto:[hidden email]]
Sent: Monday, 24 March 2008 11:51 PM
To: Lecuyer, Fabrice; Mark joshi
Cc: [hidden email]
Subject: Re: [Quantlib-users] Sobol's Low discrepency sequence

On Mar 20, 2008, at 3:06 AM, Lecuyer, Fabrice wrote:

On Mar 23, 2008, at 6:18 PM, Mark joshi wrote:

> There are two popular orderings for the polynomials in the literature.
> We need a variable to switch between the two.
>
> I reckon that JoeKuoD7 is the best.

[ Administrator note: to help keeping threads organized, when replying to a post, please use an actual "reply" and keep the subject intact.
Thanks, Luigi ]

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Mark joshi-2

Re: Sobol's Low discrepency sequence

I don't think anyone really discusses the reasoning behind their
orderings. One of the original papers (Bratley Fox) used a non-obvious
ordering which was followed for a while.
Later on, people, including Peter Jaeckel, switched to using ascending order.

The reference list in the sobolrsg.hpp is pretty comprehensive.

regards

Mark

On 25/03/2008, Lecuyer, Fabrice <[hidden email]> wrote:

> Thanks Mark.
>
> Could you please point me to a paper/book that explains the ordering for the polynomials used in QuantLib?
>
> Regards,
> Fabrice
>
> -----Original Message-----
> From: Luigi Ballabio [mailto:[hidden email]]
> Sent: Monday, 24 March 2008 11:51 PM
> To: Lecuyer, Fabrice; Mark joshi
> Cc: [hidden email]
> Subject: Re: [Quantlib-users] Sobol's Low discrepency sequence
>
>
> On Mar 20, 2008, at 3:06 AM, Lecuyer, Fabrice wrote:
> > I'm working through the implementation of the Sobol number generator
> > in QuantLib and I've got two questions on which I would appreciate any
> > insight you can give me:
> >
> > 1) At the top of the file sobolrsg.cpp a variable called
> > AltPrimitivePolynomials is set up. This variable seems to just
> > re-order some of the primitive polynomials (as compared to the order
> > in primitivepolynomials.c). Is there a theoretical reason for doing
> > this, i.e. does it improve some property of the numbers generated? I
> > haven't seen this step described in any of the literature I have read
> > on the method (e.g. Jäckel's book).
> >
> > 2) Do you have any feel for which method for initialising the free
> > direction integers provides the best results?
>
> On Mar 23, 2008, at 6:18 PM, Mark joshi wrote:
>
> > There are two popular orderings for the polynomials in the literature.
> > We need a variable to switch between the two.
> >
> > I reckon that JoeKuoD7 is the best.
>
> [ Administrator note: to help keeping threads organized, when replying to a post, please use an actual "reply" and keep the subject intact.
> Thanks, Luigi ]
>
>
> ************** IMPORTANT MESSAGE *****************************
> This e-mail message is intended only for the addressee(s) and contains information which may be
> confidential.
> If you are not the intended recipient please advise the sender by return email, do not use or
> disclose the contents, and delete the message and any attachments from your system. Unless
> specifically indicated, this email does not constitute formal advice or commitment by the sender
> or the Commonwealth Bank of Australia (ABN 48 123 123 124) or its subsidiaries.
> We can be contacted through our web site: commbank.com.au.
> If you no longer wish to receive commercial electronic messages from us, please reply to this
> e-mail by typing Unsubscribe in the subject line.
> **************************************************************
>
>
>
>

--
Quant Job Interview Questions and Answers coming very soon...

www.markjoshi.com

Assoc Prof Mark Joshi
Centre for Actuarial Studies
University of Melbourne
My website is www.markjoshi.com

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