Re: [Quantlib-dev] strange formula

[Luigi B. <lui...@gm...>]

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
> 
> 
> 

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