public void SinglePathCovariance(double[] dates, double epsilon, double precision)
{
var brownian = BrownianBridge.Create(dates);
var dim = brownian.GaussianSize(1);
var jacobian = FiniteDifferenceUtils.CenteredJacobian(x => BrownianPath1d(brownian, x), dim, new double[dim], epsilon);
var covariance = jacobian.Prod(jacobian.Tranpose());
for (int i = 0; i < dates.Length; i++)
{
for (int j = 0; j < dates.Length; j++)
{
var cov_ij = Math.Min(dates[i], dates[j]);
var error = Math.Abs(cov_ij - covariance[i, j]);
Assert.LessOrEqual(error, precision);
}
}
}
public void SinglePathIncrementCovariance(double[] dates, double epsilon, double precision)
{
var brownian = BrownianBridge.Create(dates);
var dim = brownian.GaussianSize(1);
var jacobian = FiniteDifferenceUtils.CenteredJacobian(x => PathInc1D(brownian, x), dim, new double[dim], epsilon);
var covariance = jacobian.Prod(jacobian.Tranpose());
for (int i = 0; i < dates.Length; i++)
{
var error = Math.Abs(covariance[i, i] - (i == 0 ? dates[0] : dates[i] - dates[i - 1]));
Assert.LessOrEqual(error, precision);
for (int j = 0; j < i; j++)
{
var errorij = Math.Abs(covariance[i, j]);
Assert.LessOrEqual(errorij, precision);
Assert.IsTrue(DoubleUtils.MachineEquality(covariance[i, j], covariance[j, i]));
}
}
}