Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

 Quantlet: SurfaceInterpol Description: Given a surface on a regular 2-dimensional grid, SurfaceInterpol computes the surface value at unknown points by a local polynomial interpolation

 Usage: z=SurfaceInterpol(surface,x{,h}) Input: surface Nx3 matrix, columns 1 and 2 contain x and y values of the grid, column 3 contains the z value x Mx2 matrix, containing M points at which the surface value is to be found h 2x1 vector, optional, containing the bandwidth for the local polynomial estimator; default is 30% of the range in the surface in each direction. Output: z Mx3 matrix, columns 1 and 2 contain the input parameter x, column 3 contains the computed surface values

Example:
```library("plot")
library("math")
x  = grid(#(-1,-1), #(0.1,0.1), #(40,40))
f  = exp(-0.5.*(x[,1]^2+x[,2]^2))./(2.*pi)
surface=x~f
y=(1~0.33)|(0.77~0.16)|(-0.51~0.1)|(2.3~1.3)
z=SurfaceInterpol(surface,y)
z
plot3d(1,surf,z)

```
Result:
```Produces a surface from a function of 2 arguments.
At some arbitrary points x, the surface is re-calculated by a local polynomial interpolation.

Contents of z
[1,]    -0.51      0.1  0.13887
[2,]     0.77     0.16  0.11578
[3,]        1     0.33  0.091237
[4,]      2.3      1.3  0.0046608

where the first two columns contain x, the last one the respective estimates of x.

A graphic shows the original surface (black) and the estimates (red points).
```
Example:
```library("plot")
library("finance")
library("math")
stepwidth=70|(1/52)
bandwidth=250|0.5
firstXF=3500
lastXF=7000
firstMat=0
lastMat=1
metric=1
{IVSurface,IVpoints}=volsurf(data, stepwidth,firstXF,lastXF,firstMat,lastMat, metric,bandwidth,0)
z=SurfaceInterpol(IVSurface,5000~0.15|(6000~0.16))
z
plot3d(1,IVSurface,z)

```
Result:
```In this more complex example we first fit the so called implied volatility surface.
Then the specific value of the surface at strike K=5000 and  moneyness tau=0.15,
and K=6000 and tau=0.16, is calculated:

Contents of z
[1,]     5000     0.15  0.35729
[2,]     6000     0.16   0.2995

As in the example above, a graphic shows the original surface (black) and the estimates (red points).
```

Author: M. Fengler, 20030625 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006