Re: Adding new functions to blackcalculator

Posted by Ferdinando M. Ametrano-3 on Apr 20, 2009; 11:18am
URL: http://quantlib.414.s1.nabble.com/Adding-new-functions-to-blackcalculator-tp13518p13524.html

Hi Dima

> I plan to add some new FX machinery to QuantLib.

if applicable please consider adding generic formulas to ql/pricingengines/blackformula.hpp

> In the BlackCalculator constructor we have
>  if (stdDev_>=QL_EPSILON) {
>    ...
> }    
> else{
> if (forward>strike_) {
>                 cum_d1_ = 1.0;
>                 cum_d2_= 1.0;
>             } else {
>                 cum_d1_ = 0.0;
>                 cum_d2_= 0.0;
>             }
> }
> I wonder if that's 100% right or if I've overlooked something. But if
> forward==strike,
> then we have log(f/K)=0, 
> so, if vol is not zero, we should rather have
>  cum_d1=N (0*5*stdDev_)
> which would be approximately 0.5 for very small vols. Opinions?

yeah, you're right. It should be patched as below, isn't it?

if (stdDev_>=QL_EPSILON) {
    if (close(strike_, 0.0)) {
        cum_d1_ = 1.0;
        cum_d2_ = 1.0;
        n_d1_ = 0.0;
        n_d2_ = 0.0;
    } else {
        D1_ = std::log(forward/strike_)/stdDev_ + 0.5*stdDev_;
        D2_ = D1_-stdDev_;
        CumulativeNormalDistribution f;
        cum_d1_ = f(D1_);
        cum_d2_ = f(D2_);
        n_d1_ = f.derivative(D1_);
        n_d2_ = f.derivative(D2_);
    }
} else {
    if (close(forward, strike_)) {
        cum_d1_ = 0.5;
        cum_d2_ = 0.5;
        n_d1_ = M_SQRT_2 * M_1_SQRTPI;
        n_d2_ = M_SQRT_2 * M_1_SQRTPI;
    } else if (forward>strike_) {
        cum_d1_ = 1.0;
        cum_d2_ = 1.0;
        n_d1_ = 0.0;
        n_d2_ = 0.0;
    } else {
        cum_d1_ = 0.0;
        cum_d2_ = 0.0;
        n_d1_ = 0.0;
        n_d2_ = 0.0;
    }
}

ciao -- Nando


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