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 thatseemsbasic, 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