Re: strange formula
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Nando,
following up on Chris' report (quoted below for the people on quantlib-dev joining us after the break; hi, fellows.) I tried making the correction and running the market-model test (which, it appears, is truly the only place where the formula is used, besides being exported to Excel.) The min and max errors don't change at all---I guess d*phi(h) is too low to make a difference in that case---so there's no conclusive evidence. However, some research seems to support Chris' view that the discount should be applied to both terms. Any thoughts? (or facts?) Thanks, Luigi On Tue, 2009-10-13 at 09:18 -0700, Chris Kenyon wrote: > I don't understand the bachelierBlackFormula in QL which reads (with > tests removed): > > bachelierFormula(Option::Type optionType, > Real strike, > Real forward, > Real stdDev, > Real discount) > { > ... > Real d = (forward-strike)*optionType, h = d/stdDev; > if (stdDev==0.0) > return discount*std::max(d, 0.0); > CumulativeNormalDistribution phi; > Real result = discount*stdDev*phi.derivative(h) + d*phi(h); > > return result; > } > > I think that in the result line the discount should be applied to all > the terms. There is no test in the test-suite specifically for the > bachelier. The only time it appears is in marketmodel. > > Supporting evidence comes from my own derivation (which can be wrong, > of course) and some books. In books you have to take care to include > the discounting because often they are just talking about Bachelier > (the person) who ignored interest rates. > > The other evidence is that the terms have the wrong dimensions, i.e. d > is (forward-strike) which is paid in the future but is not discounted. > Hence I don't see any way that the formula can be correct. > > I don't want to change it without some feedback but I do think it need > changing. > > Best, > Chris > > > -- Just remember what ol' Jack Burton does when the earth quakes, the poison arrows fall from the sky, and the pillars of Heaven shake. Yeah, Jack Burton just looks that big old storm right in the eye and says, "Give me your best shot. I can take it." -- Jack Burton, "Big trouble in Little China" ------------------------------------------------------------------------------ Come build with us! The BlackBerry(R) Developer Conference in SF, CA is the only developer event you need to attend this year. Jumpstart your developing skills, take BlackBerry mobile applications to market and stay ahead of the curve. Join us from November 9 - 12, 2009. Register now! http://p.sf.net/sfu/devconference _______________________________________________ QuantLib-dev mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-dev |
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On Tue, Oct 20, 2009 at 6:04 PM, Luigi Ballabio
<[hidden email]> wrote: > Any thoughts? (or facts?) I agree with the correction Chris suggested below. I just would love a confirmation from Mark, since he suggested Bachelier, even if all errors are mine :-) ciao -- Nando > On Tue, 2009-10-13 at 09:18 -0700, Chris Kenyon wrote: >> I don't understand the bachelierBlackFormula in QL which reads (with >> tests removed): >> >> bachelierFormula(Option::Type optionType, >> Real strike, >> Real forward, >> Real stdDev, >> Real discount) >> { >> ... >> Real d = (forward-strike)*optionType, h = d/stdDev; >> if (stdDev==0.0) >> return discount*std::max(d, 0.0); >> CumulativeNormalDistribution phi; >> Real result = discount*stdDev*phi.derivative(h) + d*phi(h); >> >> return result; >> } >> >> I think that in the result line the discount should be applied to all >> the terms. There is no test in the test-suite specifically for the >> bachelier. The only time it appears is in marketmodel. >> >> Supporting evidence comes from my own derivation (which can be wrong, >> of course) and some books. In books you have to take care to include >> the discounting because often they are just talking about Bachelier >> (the person) who ignored interest rates. >> >> The other evidence is that the terms have the wrong dimensions, i.e. d >> is (forward-strike) which is paid in the future but is not discounted. >> Hence I don't see any way that the formula can be correct. ------------------------------------------------------------------------------ Come build with us! The BlackBerry(R) Developer Conference in SF, CA is the only developer event you need to attend this year. Jumpstart your developing skills, take BlackBerry mobile applications to market and stay ahead of the curve. Join us from November 9 - 12, 2009. Register now! http://p.sf.net/sfu/devconference _______________________________________________ QuantLib-dev mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-dev |
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Appart from the discount question: there are different versions of the
original SDE and consequently different formulas: Page 3, Equation 2.1b: - http://www.mat.univie.ac.at/~schachermayer/pubs/preprnts/prpr0121.pdf Page 3, equation 3 - http://pascal.iseg.utl.pt/~matfin/publicar/MathFin_MRGrossinho_3.pdf - There's another one for the standard ABM in a book that I have In any case the discounting will have to be applied to both terms 2009/10/20 Ferdinando Ametrano <[hidden email]> On Tue, Oct 20, 2009 at 6:04 PM, Luigi Ballabio ------------------------------------------------------------------------------ Come build with us! The BlackBerry(R) Developer Conference in SF, CA is the only developer event you need to attend this year. Jumpstart your developing skills, take BlackBerry mobile applications to market and stay ahead of the curve. Join us from November 9 - 12, 2009. Register now! http://p.sf.net/sfu/devconference _______________________________________________ QuantLib-dev mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-dev |
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It does look wrong. All terms should be discounted equally.
I am a little surprised that the tests for Normal BGM work if the Bachelier formula is wrong. best Mark 2009/10/21 Dima <[hidden email]>: > Appart from the discount question: there are different versions of the > original SDE and consequently different formulas: > > Page 3, Equation 2.1b: > - http://www.mat.univie.ac.at/~schachermayer/pubs/preprnts/prpr0121.pdf > > Page 3, equation 3 > - http://pascal.iseg.utl.pt/~matfin/publicar/MathFin_MRGrossinho_3.pdf > > - There's another one for the standard ABM in a book that I have > > In any case the discounting will have to be applied to both terms > > > > > > 2009/10/20 Ferdinando Ametrano <[hidden email]> >> >> On Tue, Oct 20, 2009 at 6:04 PM, Luigi Ballabio >> <[hidden email]> wrote: >> > Any thoughts? (or facts?) >> I agree with the correction Chris suggested below. >> I just would love a confirmation from Mark, since he suggested >> Bachelier, even if all errors are mine :-) >> >> ciao -- Nando >> >> > On Tue, 2009-10-13 at 09:18 -0700, Chris Kenyon wrote: >> >> I don't understand the bachelierBlackFormula in QL which reads (with >> >> tests removed): >> >> >> >> bachelierFormula(Option::Type optionType, >> >> Real strike, >> >> Real forward, >> >> Real stdDev, >> >> Real discount) >> >> { >> >> ... >> >> Real d = (forward-strike)*optionType, h = d/stdDev; >> >> if (stdDev==0.0) >> >> return discount*std::max(d, 0.0); >> >> CumulativeNormalDistribution phi; >> >> Real result = discount*stdDev*phi.derivative(h) + d*phi(h); >> >> >> >> return result; >> >> } >> >> >> >> I think that in the result line the discount should be applied to all >> >> the terms. There is no test in the test-suite specifically for the >> >> bachelier. The only time it appears is in marketmodel. >> >> >> >> Supporting evidence comes from my own derivation (which can be wrong, >> >> of course) and some books. In books you have to take care to include >> >> the discounting because often they are just talking about Bachelier >> >> (the person) who ignored interest rates. >> >> >> >> The other evidence is that the terms have the wrong dimensions, i.e. d >> >> is (forward-strike) which is paid in the future but is not discounted. >> >> Hence I don't see any way that the formula can be correct. >> >> >> ------------------------------------------------------------------------------ >> Come build with us! The BlackBerry(R) Developer Conference in SF, CA >> is the only developer event you need to attend this year. Jumpstart your >> developing skills, take BlackBerry mobile applications to market and stay >> ahead of the curve. Join us from November 9 - 12, 2009. Register now! >> http://p.sf.net/sfu/devconference >> _______________________________________________ >> QuantLib-dev mailing list >> [hidden email] >> https://lists.sourceforge.net/lists/listinfo/quantlib-dev > > -- Quant Job Interview Questions and Answers is now out: www.markjoshi.com Assoc Prof Mark Joshi Centre for Actuarial Studies University of Melbourne My website is www.markjoshi.com ------------------------------------------------------------------------------ Come build with us! The BlackBerry(R) Developer Conference in SF, CA is the only developer event you need to attend this year. Jumpstart your developing skills, take BlackBerry mobile applications to market and stay ahead of the curve. Join us from November 9 - 12, 2009. Register now! http://p.sf.net/sfu/devconference _______________________________________________ QuantLib-dev mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-dev |
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On Wed, 2009-10-21 at 07:42 +1100, Mark joshi wrote:
> It does look wrong. All terms should be discounted equally. > > I am a little surprised that the tests for Normal BGM work if the > Bachelier formula is wrong. In the current test, all cases are at-the-money forward so d=0 and it doesn't matter whether d*phi(h) is discounted or not. Luigi -- No, I'm not interested in developing a powerful brain. All I'm after is just a mediocre brain, something like the president of American Telephone and Telegraph Company. -- Alan Turing on the possibilities of a thinking machine, 1943. ------------------------------------------------------------------------------ Come build with us! The BlackBerry(R) Developer Conference in SF, CA is the only developer event you need to attend this year. Jumpstart your developing skills, take BlackBerry mobile applications to market and stay ahead of the curve. Join us from November 9 - 12, 2009. Register now! http://p.sf.net/sfu/devconference _______________________________________________ QuantLib-dev mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-dev |
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