Returns the cubic spline interpolation of a function at a point.
functionValuesAtTabulationPoints[i] = f(tabulationPointsInX[i])
.functionValuesAtTabulationPoints[i] = f(tabulationPointsInX[i])
.The value of the cubic spline interpolation function at a point.
We have designed this method so that the 2nd derivatives can be pre-evaluated using the method CubicSpline2ndDifferential.
General Description of Parameters
Given the arrays tabulationPointsInX[0..n-1]
and functionValuesAtTabulationPoints[0..n-1]
,
which tabulate a function where the tabulationPointsInX
is an array where the elements are monotonically
increasing. Moreover, given the array secondDifferenttial[0..n-1]
, which is the output of the method
cubicSpline2ndDifferential
, and given a value of the interpolation points interpolationPoint
,
this method returns the value of the function at interpolationPoint
according to the cubic-spline interpolation
method.
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 XML Web service.
The values functionValuesAtTabulationPoints[0..n-1]
will refer to the expected returns of the known portfolios on the Efficient Frontier and can be evaluated using
GetEfficientFrontierExpectedReturns of the Markowitz XML Web service.
The 2nd derivatives can be thought of as the rate of change of the increase in the expected return for taken
on more risk. That is, the second derivatives express a qualitative property of the Efficient Frontier.
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.
Remarks:
Exception Type | Condition |
---|---|
InterpolationException | Thrown when the input values do not meet the requirements mentioned above. |
Interpolation Class | Portfolio Namespace | CubicSplinePointwise - this is an alternative means by which the value of the cubic spline can be evaluated at a point. Here rather than providing the 2nd differentials we are required to provide the values of the differentials at the end points. | CubicSpline2ndDifferential - use this method in order to evaluate the 2nd differentials at the tabulation points which most be provided to this method a parameter.