Re: [Quantlib-dev] strange formula

[Dima <dim...@go...>]

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 <na...@am...>

> On Tue, Oct 20, 2009 at 6:04 PM, Luigi Ballabio
> <lui...@gm...> 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
> Qua...@li...
> https://lists.sourceforge.net/lists/listinfo/quantlib-dev
>