std::complex<double> UnivariateDistribution<T>::CFImpl(double t) const
{
T leftBound = this->MinValue(), rightBound = this->MaxValue();
if (leftBound == rightBound)
return std::complex<double>(std::cos(t * leftBound), std::sin(t * leftBound));
double re = ExpectedValue([this, t] (double x)
{
return std::cos(t * x);
}, leftBound, rightBound);
double im = ExpectedValue([this, t] (double x)
{
return std::sin(t * x);
}, leftBound, rightBound);
return std::complex<double>(re, im);
}
double UnivariateDistribution<T>::Skewness() const
{
double var = Variance();
if (!std::isfinite(var))
return NAN;
double mu = Mean(); /// var is finite, so is mu
double sum = ExpectedValue([this, mu] (double x)
{
double xmmu = x - mu;
double skewness = xmmu * xmmu * xmmu;
return skewness;
}, this->MinValue(), this->MaxValue());
return sum / std::pow(var, 1.5);
}
double Black76 :: Value(
char put_call,
double forward,
double strike,
double vol,
double t,
double r)
{
double value = 0.0;
if (t <= 0 || vol <= 0) {
value = IntrinsicValue(put_call, forward, strike);
}
else {
value = exp(-(r * t)) * ExpectedValue(put_call, forward, strike, vol, t);
}
return value;
}
double UnivariateDistribution<T>::ExcessKurtosis() const
{
double var = Variance();
if (!std::isfinite(var))
return NAN;
double mu = Mean(); /// var is finite, so is mu
double sum = ExpectedValue([this, mu] (double x)
{
double xmmu = x - mu;
double kurtosisSqrt = xmmu * xmmu;
double kurtosis = kurtosisSqrt * kurtosisSqrt;
return kurtosis;
}, this->MinValue(), this->MaxValue());
return sum / (var * var) - 3;
}
