CreditRisk+ Model - recursive algorithm (Help)

[akbar]

Hi,
I am trying to implement CreditRisk+ model in Matlab but I am facing some issues with the recursive algorithm used in the model. So, I am hopeful that some of you may assist me in this regard.

I am following the technical document of the CreditRisk+ model which I took from defaultrisk.com. As mentioned on page 48 of the document (attached) I will use some equations to highlight my question.

As stated in equation (69) the (G(z)=\sum_{n=0}^{inf}A_{n}Z^{n})

shows the power series which satisfy the differential equation;
(\frac{d}{dz}log(G(z))=\frac{1}{G(z)}\frac{dG(z)}{dZ}=\frac{A(z)}{B(z)})

Moreover, (A(z)=a_{o}+....+a_{r}z^{r}) and
(B(z)=b_{o}+....+b_{s}z^{s})

My question is how to derive equation (72)
(A_{n+1}=\frac{1}{b_{o}(n+1)}[\sum_{i=0}^{min(r,n)}a_{j}A_{n-j}-\sum_{j=0}^{min(s-1,n-1)}b_{j+1}(n-j)A_{n-j}])

Thanking you for your time.
Regards,

 

[chaoticrambler]

What do you not understand in the derivation ? All you have to do is compare coefficients of powers of z on both sides of equations 73. The derivation is given right below the formula in the pdf you posted.

 

[mrmelchi]

Try the following paper:

http://papers.ssrn.com/abstract=1122844

I hope it helps.

Mario

 

[Mr Doe]

Fourier transfrom is a huge overkill in this case.
The only thing that explicitly isn't stated in the derivation of the equation is the product rule for series (you can find it here -> http://en.wikipedia.org/wiki/Power_series). You can identify a polynomial as a series with the coefficients higher than s, that is r, that equal zero.
It would be best if the original poster would explicitly say what's bothering him with the derivation.