Thread: Cubic interpolation

Helle there,

I am currently studying fixed-income market securities as part of a master's degree in Finance, but I seem to have a problem that involves understanding something that seems basic, but since I lack knowledge of any form of Matrix' solving, I suppose the question will do just fine in the Pre-University Math Help forums.

I need to find the interpolated rate R(0,w) with w [v;z] verifieying the three-order polynomial equation: R(0,w) = aw^3 + bw^2 + cw + d

where a, b, c and d sitisfy the system:

R(0,v) = av^3 + bv^2 + cv + d
R(0,x) = ax^3 + bx^2 + cx + d
R(0,y) = ay^3 + by^2 + cy + d
R(0,z) = az^3 + bz^2 + cz + d

I need to solve this cubic polynomial function by solving a matrix:

a
b
c
d

equals

1 1 1 1
8 4 2 1
27 9 3 1
64 16 4 1

by

3%
5%
5,5%
6%


Then what I don't understand, is that it (my book) shows me solve for the vector of constants a, b, c and d by:

x = B^(-1)*A, where x are the constant, B the matrix of maturity terms and A the vector of interest rate (3%, 5%, etc.).

The answers are:
0.0025
-0.0225
0.07
-0.02

I might not even need to know this, but I am currently deeply frustrated by not being able to understand this

Who can help me out here?

Regards,

Hans

Since you have the formula which uses the "inverse" of B, do you know how to find the inverse of a matrix? Or do you know how to do "row reduction" of a matrix?

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