//Cumulative Normale
double CN(double x){
static double a[5] = {0.319381530, -0.356563782, 1.781477937, -1.821255978, 1.330274429};
double result;
if(x<-7.0) result = NormalDensity(x) / sqrt(1.+x*x);
else{
if(x>7.0) result = 1.0 - CN(-x);
else{
double tmp = 1.0 / (1.0+0.2316419*fabs(x));
result = 1 - NormalDensity(x)* (tmp*(a[0]+tmp*(a[1]+tmp*(a[2]+tmp*(a[3]+tmp*a[4])))));
if(x<=0.0) result = 1.0 - result;
}
}
return result;
}
double BlackAndScholes( double dRateDomestic,
double dRateForeign,
double dHTBRate,
double dSpotPrice,
double dStrike,
double dYte,
double dVolatility,
bool bIsCall,
double* pdDivAmnt,
double* pdDivYte,
int nDivCount,
GREEKS* pGreeks/*out*/)
{
if (dYte < 0.)
return max(bIsCall ? dSpotPrice - dStrike : dStrike - dSpotPrice, 0.);
double dContRd = RateDiscToCont(dRateDomestic , dYte * cdDaysPerYear365);
double dContRf = RateDiscToCont(dRateForeign, dYte * cdDaysPerYear365);
//double dContRb = IsBadValue(dHTBRate) ? 0 : (dContRd - RateDiscToCont(dHTBRate, nDte)); //actual stock borrowing rate (b in spec)
double dContRb = IsBadValue(dHTBRate) ? 0 : (RateDiscToCont(dRateDomestic - dHTBRate, dYte * cdDaysPerYear365)); //actual stock borrowing rate (b in spec)
double dDiscountedSpot = DiscountForDividends(dSpotPrice,
dContRd,
dContRb,
pdDivAmnt,
pdDivYte,
nDivCount,
dYte);
if(IsBadValue(dDiscountedSpot))
return BadDoubleValue;
const double A = dDiscountedSpot * (1. / exp( (dContRf + dContRb) * dYte));
const double B = dStrike * (1. / exp( dContRd * dYte));
const double D = dVolatility * sqrt(dYte);
const double d1 = log(dDiscountedSpot/dStrike) / D + D * (((dContRd - (dContRf + dContRb)) / (dVolatility * dVolatility)) + .5);
const double d2 = d1 - D;
const double N1 = NormalC(d1);
const double N2 = NormalC(d2);
long cCalculatedGreeksMask = GT_NOTHING;
double dTheoPrice = bIsCall ? A * N1 - B * N2 : A * ( N1 - 1.) - B * ( N2 - 1.);
if(!IsValidTheoPrice(dTheoPrice))
{
dTheoPrice = BadDoubleValue;
}
else
{
cCalculatedGreeksMask |= GT_THEOPRICE;
}
if(pGreeks && pGreeks->nMask & ~GT_THEOPRICE && !IsBadValue(dTheoPrice))
{
const double dd1dS = 1. / (D * dDiscountedSpot);
const double dd1dT = -d2 / (2. * dYte) + (dContRd - (dContRf + dContRb)) / D;
const double dd2dT = -d1 / (2. * dYte) + (dContRd - (dContRf + dContRb)) / D;
const double dd1dVol = - d2 / dVolatility;
const double dd2dVol = - d1 / dVolatility;
const double dd12dR = dYte / D;
const double d2d1dVol2 = 2 * log(A/B) / (D * dVolatility * dVolatility);
const double n1 = NormalDensity(d1);
const double n2 = NormalDensity(d2);
// DELTA
if (pGreeks->nMask & GT_DELTA)
{
pGreeks->dDelta = exp(-(dContRf + dContRb) * dYte) * (N1 - (bIsCall ? 0. : 1.));
cCalculatedGreeksMask |= GT_DELTA;
}
// GAMMA
if (pGreeks->nMask & GT_GAMMA)
{
pGreeks->dGamma = exp(-(dContRf + dContRb) * dYte) * dd1dS * n1;
cCalculatedGreeksMask |= GT_GAMMA;
}
// THETA
if (pGreeks->nMask & GT_THETA)
{
pGreeks->dTheta = ( A * ((dContRf + dContRb) * (N1 - (bIsCall ? 0. : 1.)) - dd1dT * n1) -
B * (dContRd * (N2 - (bIsCall ? 0. : 1.)) - dd2dT * n2) ) * cdDeltaTime;
cCalculatedGreeksMask |= GT_THETA;
}
// DELTA THETA
if (pGreeks->nMask & GT_DELTA_THETA)
{
pGreeks->dDeltaTheta = ( (dContRf + dContRb) * (pGreeks->dDelta - (bIsCall ? 0. : exp(-(dContRf + dContRb) * dYte) )) -
pGreeks->dGamma * dd1dT / dd1dS ) * cdDeltaTime;
cCalculatedGreeksMask |= GT_DELTA_THETA;
}
// GAMMA THETA
if (pGreeks->nMask & GT_GAMMA_THETA)
{
pGreeks->dGammaTheta = ( pGreeks->dGamma * ((dContRf + dContRb) + 1. / (2. * dYte) + d1 * dd1dT) ) * cdDeltaTime;
cCalculatedGreeksMask |= GT_GAMMA_THETA;
}
// DELTA VEGA
if (pGreeks->nMask & GT_DELTA_VEGA)
{
pGreeks->dDeltaVega = ( pGreeks->dGamma * dd1dVol / dd1dS ) * cdDeltaVolatility;
cCalculatedGreeksMask |= GT_DELTA_VEGA;
}
// GAMMA VEGA
if (pGreeks->nMask & GT_GAMMA_VEGA)
{
pGreeks->dGammaVega = ( -pGreeks->dGamma * ( 1. / dVolatility + d1 * dd1dVol) ) * cdDeltaVolatility;
cCalculatedGreeksMask |= GT_GAMMA_VEGA;
}
// VEGA
if (pGreeks->nMask & GT_VEGA)
{
pGreeks->dVega = ( A * dd1dVol * n1 - B * dd2dVol * n2 ) * cdDeltaVolatility;
cCalculatedGreeksMask |= GT_VEGA;
}
// RHO
if (pGreeks->nMask & GT_RHO)
{
pGreeks->dRho = ( (A * n1 - B * n2) * dd12dR + dYte * B * (N2 - (bIsCall ? 0. : 1.)) ) * cdDeltaRate;
cCalculatedGreeksMask |= GT_RHO;
}
// VOLGA
if (pGreeks->nMask & GT_VOLGA)
{
pGreeks->dVolga = (A * n1 * (-d1 * (dd1dVol * dd1dVol) + d2d1dVol2) -
B * n2 * (-d2 * (dd2dVol * dd2dVol) + d2d1dVol2)) * cdDeltaVolatility * cdDeltaVolatility;
cCalculatedGreeksMask |= GT_VOLGA;
}
// Check values
if (cCalculatedGreeksMask & GT_DELTA)
pGreeks->dDelta = min(max(pGreeks->dDelta, -1.), 1.);
if (cCalculatedGreeksMask & GT_GAMMA)
pGreeks->dGamma = max(pGreeks->dGamma, 0.);
if (cCalculatedGreeksMask & GT_VEGA)
pGreeks->dVega = max(pGreeks->dVega, 0.);
if (cCalculatedGreeksMask & GT_THETA)
pGreeks->dTheta = min(pGreeks->dTheta, 0.);
// ALPHA
if ((pGreeks->nMask & GT_ALPHA) && (ValueNEQZero(pGreeks->dTheta)))
{
pGreeks->dAlpha = pGreeks->dGamma / pGreeks->dTheta;
cCalculatedGreeksMask |= GT_ALPHA;
}
}
// Set up greeks mask
if(pGreeks)
pGreeks->nMask = cCalculatedGreeksMask;
return dTheoPrice;
}
