Low Default Portfolio (PD)

 Modeling Low Default Portfolio (Independent Default Events):

Pluto and Tasche method for calculating probability of default for portfolios with none or very few observations of defaults.
One-sided upper confidence bound as an estimator of PD.

Assumptions:
- n >0 borrowers in the portfolio.
- At the end of the observation period 0≤ d < n defaults are observed among the n borrowers.
- Default events are independent, hence the number of defaults in a portfolio is binomially distributed:
nCr * p^r * ((1-p)^(n-r)
n is the total number of borrowers, r is the total number of defaults and p is the probability of default.
PD to be logical, it should have the following characteristic:
p1 <= p2 <=p3 <=p4..........
It also means that p1=p2=p3=p4=p5...... In this scenario, all the 500 borrowers belong to the same risk characteristic, i.e. homogenous borrowers.

E.g: 

https://drive.google.com/file/d/1OmGmQV-AsYPsfdRYowSy1bkZArgEFMvN/view?usp=sharing