Value-at-Risk Theory and Practice

The first advanced book on value-at-risk

Chapter 2, Page 67
Exercise 5

Interpolate a function of the form

[51]

such that f (1, 0) = 1 and f (1, 1) = 1.

Solution

Let

  • f1(x1, x2) = exp(x1 + x2)

  • f2(x1, x2) = exp(x1 – x2)

Then

[s1]

and

[s2]

We seek

[s3]

such that

[2.48]

This is obtained as

[s4]

Our interpolated polynomial is

f(x1, x2) = .0989 exp(x1 + x2) + .2689 exp(x1 + x2)

[s5]

 
 

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