cum_normal.cc

Financial Recipes

// numerical approximations to univariate N(z) cumulative normal distribution

#include <cmath>     // math functions.
using namespace std;

double N(double z) {
// This is a numerical approximation to the normal distribution.  
// See Abramowitz and Stegun: Handbook of Mathemathical functions
// for description.  The arguments to the functions are assumed 
// normalized to a (0,1 ) distribution. 

    if (z >  6.0) { return 1.0; }; // this guards against overflow 
    if (z < -6.0) { return 0.0; };

    double b1 =  0.31938153; 
    double b2 = -0.356563782; 
    double b3 =  1.781477937;
    double b4 = -1.821255978;
    double b5 =  1.330274429; 
    double p  =  0.2316419; 
    double c2 =  0.3989423; 

    double a=fabs(z); 
    double t = 1.0/(1.0+a*p); 
    double b = c2*exp((-z)*(z/2.0)); 
    double n = ((((b5*t+b4)*t+b3)*t+b2)*t+b1)*t; 
    n = 1.0-b*n; 
    if ( z < 0.0 ) n = 1.0 - n; 
    return n; 
};