double BS::callFXOptionPrice() const{
double cdfn1 = normalCDF(d1);
double cdfn2 = normalCDF(d2);
return S*exp(-rf*(T-t))*cdfn1 - E*exp(-rd*(T-t))*cdfn2;
}
double BS::putFXOptionPrice() const{
double cdfn1 = normalCDF(-d1);
double cdfn2 = normalCDF(-d2);
return E*exp(-rd*(T-t))*cdfn2 - S*exp(-rf*(T-t))*cdfn1;
}
// Compute gamma cdf by a normal approximation
static double gnorm(double a, double x)
{
double p, sx;
if (x <= 0.0 || a <= 0.0)
return 0.0;
else {
sx = sqrt(a) * 3.0 *
(pow(x / a, 1.0 / 3.0) + 1.0 / (a * 9.0) - 1.0);
return normalCDF(sx);
}
}
static double normalizer(const Param &a, const Param &b) {
double p1 = a.p;
double p2 = b.p;
double u1 = a.u;
double u2 = b.u;
double s1 = a.s;
double s2 = b.s;
double sum = 0;
for(int r1=-6; r1 <=6; r1++) {
for(int r2=-6; r2 <=6; r2++) {
double u1_n = u1+r1*2*PI;
double u2_n = u2+r2*2*PI;
double top = exp(-0.5*((u1_n-u2_n)*(u1_n-u2_n))/(s1*s1+s2*s2));
double bot = sqrt(2*PI*(s1*s1+s2*s2));
double u_new = (u1_n*s2*s2+u2_n*s1*s1)/(s2*s2+s1*s1);
double s_new = (s1*s2)/sqrt(s1*s1+s2*s2);
sum += (top/bot) * (normalCDF(PI,u_new,s_new)-normalCDF(-PI,u_new,s_new));
}
}
return p1*p2*sum;
}
/**
* @brief Normal cumulative distribution function: In-database interface
*/
AnyType
normal_cdf::run(AnyType &args) {
return normalCDF(args[0].getAs<double>());
}
