Interpolation Function

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Interpolation Function

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The Interpolation function calculates the linear or cubic-spline interpolated Y value based on a desired X value and a range of known X and Y values. The interpolation function can be used in conjunction with the various option models.

 

 

Interpolation

(InterpolationType, Xrange, Yrange, ValueX)

 

Argument

Description

InterpolationType

Alphanumeric value indicating the interpolation type or model:

Linear = 0 or "L" (case insensitive)

Cubic Spline = 1 or "C" (case insensitive)

Xrange

The range of ascending and unique (non-duplicate) known X values. The size of the array, i.e. the number of values within it, must be the same as the Yrange array.

Yrange

The range of known Y values, where the size of the array must be the same as the Xrange.

ValueX

The input value for the X coordinate whereby a Y value is desired and the return value of the function.

 

 

Example

Example: Linear and Cubic Spline Interpolation

Calculate the linear and cubic spline interpolation and graph the results give the following table of known X and Y values at the Desired X values below. So,

 

Input

 

Output

Known X

Known Y

 

Desired X

Linear Interpolation

Cubic Spline Interpolation

0.500

3.250

 

0.500

3.250

3.250

1.000

3.625

 

1.500

3.792

3.865

2.500

4.125

 

2.500

4.125

4.125

4.750

4.375

 

3.500

4.236

4.426

6.250

3.250

 

4.500

4.347

4.464

9.500

3.125

 

5.500

3.813

3.853

 

 

 

6.500

3.240

3.099

 

 

 

7.500

3.202

2.807

 

 

 

8.500

3.163

2.875

 

 

 

9.500

3.125

3.125

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See Also

Historical Volatility