I could not find any such detailed documentation after some weeks of looking (not non-stop obviously). It is appallingly documented. I do understand fully what it does though so am happy to field some questions on it if you like.

In a nutshell, I can tell you it is a standard reduced-form credit model under a constant hazard rate (i.e. homogeneous Poisson process). As such it assumes that the default-intensity is not stochastic and is therefore totally unsuitable for any type of quant modelling. 

In fact, it is not intended for modelling but only serves as a market-standard converter from Quoted Spreads to CDS Upfront. Somewhat analogously to Black-Scholes Implied Vol, nobody thinks that the underlying follows a simple drift diffusion - IV is only a quoting mechanism for option "value". 

It is the Upfront $UF = (S_{ISDA}-C)RPV01_{ISDA}$ that is the market-value of the CDS contract and the Quoted Spreads are only a quoting convention which, in conjunction with the ISDA Standard Converter produce that Upfront mark-to-market - (in this way, Quoted Spreads $S_{ISDA}$ are specifically intended for ISDA "Model" $RPV01_{ISDA}$ Conversion). 

You could equally come up with your own model (based on say a CIR intensity diffusion) which would have its own spreads $S_{CIR}$ (different to the market quoted spreads) but MUST convert via $RPV01_{CIR}$ to the same Upfront $UF$ which is the value actually exchanged in trading. 

$(S_{CIR}-C)RPV01_{CIR} = UF = (S_{ISDA}-C)RPV01_{ISDA}$

Outside of the spread-to-upfront conversion the "model" has no (intended or practical) usefulness at all.

Read  [Damiano Brigo][1] and also the Barclays' "STANDARD CORPORATE CDS HANDBOOK" (2010).

I have a Matlab mex file of the ISDA Source Code Converter which I would happily share with you, but you will need to parse the ISDA Swap Fixings XML Files yourself, to reproduce exactly what you see on Bloomberg CDSW

Best Rgds,
Mark

  [1]: http://www.damianobrigo.it/cdsbigbang.pdf