Returns the value of the cubic spline interpolation at a given point.
functionValuesAtTabulationPoints[i] = f(tabulationPointsInX[i])
.functionValuesAtTabulationPoints[i] = f(tabulationPointsInX[i])
, where f
is the function being considered.tabulationPointsInX[0]
.tabulatedPointInX[n-1]
.The value of the cubic spline interpolation function at a point.
General Description of Parameters
Given a function which is tabulated at the points tabulationPointsInX[0..n-1]
which has elements was are monotonically increasing and takes the values
functionValuesAtTabulationPoints[0..n-1]
at those points, this methods returns
the values of the cubic spline interpolation function evaluated at the
given point interpolationPoint
.
Description of the Parameters in terms of the Efficient Frontier
With direct regards to the Efficient Frontier the points tabulationPointsInX[0..n-1]
,
will refer to the risk of the portfolios on the Efficient Frontier and be evaluated using
GetEfficientFrontierPortfolioRisks of the Markowitz class.
The values functionValuesAtTabulationPoints[0..n-1]
will refer to the expected returns of the known portfolios on the Efficient Frontier and be evaluated using
GetEfficientFrontierExpectedReturns of the Markowitz class.
The point at which the cubic spline in interpolated namely, interpolationPoint
, will refer
to the value of the portfolio risk for which the value of corresponding expected return will be returned.
Notes on Estimating the Derivatives
When applying this method you will need to provide values of the derivative of the interpolation function at the end points. A reasonable estimate with regard to approximating the Efficient Frontier could be provided by directed evaluating the slope between either the first or last two known points of the Efficient Frontier.
Remark: If the two arrays have different lengths, the shorter one will be used as reference. The two arrays should be at least 2 elements long.
Exception Type | Condition |
---|---|
InterpolationException | Thrown when the input values do not meet the requirements mentioned above. |
Interpolation Class | WebCab.COM.Finance.Portfolio Namespace | CubicSplinePointwisePreEvaluation