Posted by
Bennett, Paul-2 on
URL: http://quantlib.414.s1.nabble.com/Issues-with-Gauss-Hermite-Integration-tp6680p6683.html
I found Gauss-Legendre integration to be much more consistent and stable than Gauss-Hermite. This is better because you integrate over the region [a,b] rather than (- infinity, +infinity). Do you really need to integrate over (- infinity, +infinity), usually you can restrict this, you may find that considering (-5,+5) is good enough, think of the Normal distribution.
You can also split the integral into many sub-integrals as you like, use the Gauss-Legendre integration to do each sub-interval and then sum up the total for the whole integral.
Regards,
Paul
Dr. Paul Bennett
Quantitative Analyst
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http://www.LBBWsg.com-----Original Message-----
From: Yomi [mailto:
[hidden email]]
Sent: Wednesday, September 24, 2008 10:40 PM
To:
[hidden email]
Subject: Re: [Quantlib-users] Issues with Gauss Hermite IntegrationHi
Thanks Klaus,
I guess I could live with 40 steps integration for the moment.
Regards
Klaus Spanderen-2 wrote:
>
> Hi
>
> I've noticed a similar behaviour when using the Heston pricing engine with
> a
> Gauss-Laguerre integration of order > 200. I guess switching towards
> Gauss-Lobatto will help if you really need more accuracy than a
> Gauss-Hermite
> integration of order 40 provides.
>
> cheers
> Klaus
>
> On Tuesday 23 September 2008 10:58:55 Yomi wrote:
>> Hi,
>>
>> I have added a model that requires FFT for price vanillas.
>> The integral needs for be computed from -inf to inf, so the choice of
>> GaussHermiteIntegration.
>> I have seen that increasing the integration order leads to very high
>> weights which give totaly wrong numbers.
>> I have found that the optimal number should be around 40. If we go to 64
>> or
>> 128, the results are negative due to the heavy weights.
>> Does it make sense to you? Is there something I am missing?
>>
>> Cheers
>
>
>
> --
> Klaus Spanderen
> Ludwig Erhard Str. 12
> 48734 Reken (Germany)
> EMail:
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