
Cubic interpolation
Helle there,
I am currently studying fixedincome 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 PreUniversity Math Help forums.
I need to find the interpolated rate R(0,w) with w [v;z] verifieying the threeorder 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

Re: Cubic interpolation
Since you have the formula $\displaystyle x= B^{1}A$ 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?
You might find these interesting:
[‪Determining Inverse Matrices Using Augmented Matrices‬‏  YouTube32.3 The Inverse of a Matrix