Re: [Quantlib-dev] strange formula

[Ferdinando A. <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.