private double A(double eta)
{
bool differentStartOfLookback = lookbackPeriodStartTime().IsNotEqual(residualTime());
double carry = riskFreeRate() - dividendYield();
double vol = volatility();
double x = 2.0 * carry / (vol * vol);
double s = underlying() / strike();
double ls = Math.Log(s);
double d1 = ls / stdDeviation() + 0.5 * (x + 1.0) * stdDeviation();
double d2 = d1 - stdDeviation();
double e1 = 0, e2 = 0;
if (differentStartOfLookback)
{
e1 = (carry + vol * vol / 2) * (residualTime() - lookbackPeriodStartTime()) / (vol * Math.Sqrt(residualTime() - lookbackPeriodStartTime()));
e2 = e1 - vol * Math.Sqrt(residualTime() - lookbackPeriodStartTime());
}
double f1 = (ls + (carry + vol * vol / 2) * lookbackPeriodStartTime()) / (vol * Math.Sqrt(lookbackPeriodStartTime()));
double f2 = f1 - vol * Math.Sqrt(lookbackPeriodStartTime());
double n1 = f_.value(eta * d1);
double n2 = f_.value(eta * d2);
BivariateCumulativeNormalDistributionWe04DP cnbn1 = new BivariateCumulativeNormalDistributionWe04DP(-1),
cnbn2 = new BivariateCumulativeNormalDistributionWe04DP(0),
cnbn3 = new BivariateCumulativeNormalDistributionWe04DP(0);
if (differentStartOfLookback)
{
cnbn1 = new BivariateCumulativeNormalDistributionWe04DP(-Math.Sqrt(lookbackPeriodStartTime() / residualTime()));
cnbn2 = new BivariateCumulativeNormalDistributionWe04DP(Math.Sqrt(1 - lookbackPeriodStartTime() / residualTime()));
cnbn3 = new BivariateCumulativeNormalDistributionWe04DP(-Math.Sqrt(1 - lookbackPeriodStartTime() / residualTime()));
}
double n3 = cnbn1.value(eta * (d1 - x * stdDeviation()), eta * (-f1 + 2.0 * carry * Math.Sqrt(lookbackPeriodStartTime()) / vol));
double n4 = cnbn2.value(eta * e1, eta * d1);
double n5 = cnbn3.value(-eta * e1, eta * d1);
double n6 = cnbn1.value(eta * f2, -eta * d2);
double n7 = f_.value(eta * f1);
double n8 = f_.value(-eta * e2);
double pow_s = Math.Pow(s, -x);
double carryDiscount = Math.Exp(-carry * (residualTime() - lookbackPeriodStartTime()));
return(eta * (underlying() * dividendDiscount() * n1
- strike() * riskFreeDiscount() * n2
+ underlying() * riskFreeDiscount() / x
* (-pow_s * n3 + dividendDiscount() / riskFreeDiscount() * n4)
- underlying() * dividendDiscount() * n5
- strike() * riskFreeDiscount() * n6
+ carryDiscount * dividendDiscount()
* (1 - 0.5 * vol * vol / carry) *
underlying() * n7 * n8));
}
private double A(double eta)
{
bool fullLookbackPeriod = lookbackPeriodEndTime().IsEqual(residualTime());
double carry = riskFreeRate() - dividendYield();
double vol = volatility();
double x = 2.0 * carry / (vol * vol);
double s = underlying() / minmax();
double ls = Math.Log(s);
double d1 = ls / stdDeviation() + 0.5 * (x + 1.0) * stdDeviation();
double d2 = d1 - stdDeviation();
double e1 = 0, e2 = 0;
if (!fullLookbackPeriod)
{
e1 = (carry + vol * vol / 2) * (residualTime() - lookbackPeriodEndTime()) / (vol * Math.Sqrt(residualTime() - lookbackPeriodEndTime()));
e2 = e1 - vol * Math.Sqrt(residualTime() - lookbackPeriodEndTime());
}
double f1 = (ls + (carry + vol * vol / 2) * lookbackPeriodEndTime()) / (vol * Math.Sqrt(lookbackPeriodEndTime()));
double f2 = f1 - vol * Math.Sqrt(lookbackPeriodEndTime());
double l1 = Math.Log(lambda()) / vol;
double g1 = l1 / Math.Sqrt(residualTime());
double g2 = 0;
if (!fullLookbackPeriod)
{
g2 = l1 / Math.Sqrt(residualTime() - lookbackPeriodEndTime());
}
double n1 = f_.value(eta * (d1 - g1));
double n2 = f_.value(eta * (d2 - g1));
BivariateCumulativeNormalDistributionWe04DP cnbn1 = new BivariateCumulativeNormalDistributionWe04DP(1),
cnbn2 = new BivariateCumulativeNormalDistributionWe04DP(0),
cnbn3 = new BivariateCumulativeNormalDistributionWe04DP(-1);
if (!fullLookbackPeriod)
{
cnbn1 = new BivariateCumulativeNormalDistributionWe04DP(Math.Sqrt(lookbackPeriodEndTime() / residualTime()));
cnbn2 = new BivariateCumulativeNormalDistributionWe04DP(-Math.Sqrt(1 - lookbackPeriodEndTime() / residualTime()));
cnbn3 = new BivariateCumulativeNormalDistributionWe04DP(-Math.Sqrt(lookbackPeriodEndTime() / residualTime()));
}
double n3 = cnbn1.value(eta * (-f1 + 2.0 * carry * Math.Sqrt(lookbackPeriodEndTime()) / vol), eta * (-d1 + x * stdDeviation() - g1));
double n4 = 0, n5 = 0, n6 = 0, n7 = 0;
if (!fullLookbackPeriod)
{
n4 = cnbn2.value(-eta * (d1 + g1), eta * (e1 + g2));
n5 = cnbn2.value(-eta * (d1 - g1), eta * (e1 - g2));
n6 = cnbn3.value(eta * -f2, eta * (d2 - g1));
n7 = f_.value(eta * (e2 - g2));
}
else
{
n4 = f_.value(-eta * (d1 + g1));
}
double n8 = f_.value(-eta * f1);
double pow_s = Math.Pow(s, -x);
double pow_l = Math.Pow(lambda(), x);
if (!fullLookbackPeriod)
{
return(eta * (underlying() * dividendDiscount() * n1 -
lambda() * minmax() * riskFreeDiscount() * n2 +
underlying() * riskFreeDiscount() * lambda() / x *
(pow_s * n3 - dividendDiscount() / riskFreeDiscount() * pow_l * n4)
+ underlying() * dividendDiscount() * n5 +
riskFreeDiscount() * lambda() * minmax() * n6 -
Math.Exp(-carry * (residualTime() - lookbackPeriodEndTime())) *
dividendDiscount() * (1 + 0.5 * vol * vol / carry) * lambda() *
underlying() * n7 * n8));
}
else
{
//Simpler calculation
return(eta * (underlying() * dividendDiscount() * n1 -
lambda() * minmax() * riskFreeDiscount() * n2 +
underlying() * riskFreeDiscount() * lambda() / x *
(pow_s * n3 - dividendDiscount() / riskFreeDiscount() * pow_l * n4)));
}
}
