In particular,
we offer methods based around the cubic interpolation (recommended approach)
and polynomial interpolation procedures. This XL Service contains several
methods for constructing continuous functions from discrete data points.
Such methods are generally referred to as Interpolation and Extrapolation
methods.
Functionality Offered
With this XL Service we offer the following functionality:
Polynomial Interpolation
InterpolateExtrapolatePolynomial - returns the value and an error
estimate of an interpolation point where the interpolation function is a polynomial
of a given order.
CoefficientsInterpolatingPolynomialStable - this method is similar to
the approach given above except that here we have a higher level of stability which
we pay for with lower efficiency.
CubicSplinePointwise - Evaluates the cubic spline interpolation constructed from a given
set of points. When applying this method you will need to give the values of the derivatives at the end
points. A reasonable estimate could be provided by directed evaluation of the slope between either the
first or last two known points of the Efficient Frontier.
How to construct the Efficient Frontier using Interpolation
As mentioned above the main aim of these interpolation procedures is to provide the means
by which the Efficient Frontier can be constructed from a finite set of points on which it
can be evaluated by using the method: CalculateEfficientFrontier from Markowitz XL Service.
The expected return and risk coordinate components of these points can then be read off by using
the methods GetEfficientFrontierExpectedReturns and
GetEfficientFrontierPortfolioRisks from Markowitz XL Service.
Once the interpolation points are known we are able to construct the interpolation around
these points and then in the case of cubic spline interpolation evaluate the Efficient Frontier
at an arbitrary value points by using one of the methods: CubicSplinePointwise,
CubicSplinePointwisePreEvaluation.