# Fitting survival/hazard model to probability of default

I will very grateful with some help on the following problem: I need to forecast probability of default for portfolio of retail loans, depending on several factors, that can be divided into three groups: first group – is initial conditions during the perdio, when these loans were issued (these factors are fixed in time, but vary among different months of issuing), second group is macroeconomic factors that vary during the life of the loans, and third factor depends to time trend. I have aggregated data, with only total figures for loans issued in particular month (not for each loan separately). I have tried to use survival analysis to estimate this problem, but with little result so far. I used the following approach: for simplicity I dropped time varying components and focused on initial conditions and time factor. Loans issued in different months can be viewed as different portfolios (vintages), and as time goes the share of bad loans in each vintage is increasing with diminishing speed. The data structure is following: new bad loans in the portfolio issued particular month

(Month passed)  (Loans issued in Jan 2000) (Loans issued in Feb 2000) …
1                0.15%                     0.12%
2                0.09%                     0.10%
3                0.05%                     0.08%
4                0.03%                     0.06%


The shape of the curve for each vintage resembles some hazard/survival function, so I tried to fit is with Weibull/Gamma and some other probability function, but with little result. I quite newcomer in survival analysis or risk management, so maybe there are some methods or algorithms that are usually used to handle such problems that I’m not aware about. I will very appreciate any suggestions or links to material where I can find some solutions and it will also be great if there is some available methods for estimation in matlab or R.