Estimation of Probability of Defaults (PD) for Low Default Portfolios: An actuarial Approach

Original by Nabil Iqbal, Syed Afraz Ali, 2012, 18 pages 

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  • Use mechanism of “convolution”
  • Use Bayesian theorem for the weight  of default for each grade, i.e. the probability that  a default occurred in a specific grade
  • Use the binomial distribution to predict the probability that the number of defaults differs from the number of defaults in the grade
  • Use then Poisson distribution to take into account the number of customers in each grade to generate a frequency distribution
  • The use a convolution mode to combine the information and produce de matrix (how it is done is not clear)
  • PD depend on number of customers in grades and changes over time. As such it is dynamic. How it is applied in practice is not clear