Issues with Gauss Hermite Integration
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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 |
Re: Issues with Gauss Hermite IntegrationHi
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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: [hidden email] (remove NOSPAM from the address) ------------------------------------------------------------------------- This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the world http://moblin-contest.org/redirect.php?banner_id=100&url=/ _______________________________________________ QuantLib-users mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-users |
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Thanks Klaus,
I guess I could live with 40 steps integration for the moment. Regards
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Re: Issues with Gauss Hermite IntegrationHi
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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 Capital Markets and Treasury Landesbank Baden-Württemberg Singapore Branch 25 International Business Park #01-72 German Centre Singapore 609916 Telephone: +65 6562-9255 Telefax: +65 6562-9259 mailto: [hidden email] 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: [hidden email] (remove NOSPAM from the address) > > ------------------------------------------------------------------------- > This SF.Net email is sponsored by the Moblin Your Move Developer's > challenge > Build the coolest Linux based applications with Moblin SDK & win great > prizes > Grand prize is a trip for two to an Open Source event anywhere in the > world > http://moblin-contest.org/redirect.php?banner_id=100&url=/ > _______________________________________________ > QuantLib-users mailing list > [hidden email] > https://lists.sourceforge.net/lists/listinfo/quantlib-users > > -- View this message in context: http://www.nabble.com/Issues-with-Gauss-Hermite-Integration-tp19623807p19650401.html Sent from the quantlib-users mailing list archive at Nabble.com. ------------------------------------------------------------------------- This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the world http://moblin-contest.org/redirect.php?banner_id=100&url=/ _______________________________________________ QuantLib-users mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-users ------------------------------------------------------------------------- This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the world http://moblin-contest.org/redirect.php?banner_id=100&url=/ _______________________________________________ QuantLib-users mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-users |
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