Member-only story
Jeffrey’s Test and Prescribed Analysis
Prescribed analysis can be testing.
Regulations and standards may prescribe certain kinds of analysis. This is a common facet of financial services regulation and guidance.
Financial institutions have models which use internal ratings. Those models help set the buffer needed to absorb losses under stress. ‘Capital’ is the term for this financial cushion.
The European Central Bank gives guidance on how to test these internal models. Financial firms lend to people or other institutions. These ‘obligors’ may fail to pay back their loans on time, going into ‘default’ on those loans.
Some models then estimate the probability of default in different grades. The guidance asks analysts to perform Jeffrey’s test to assess the model predictions:
Given the Jeffreys prior for the binomial proportion, the posterior distribution is a beta distribution with shape parameters a = D + 1/2 and b = N — D + 1/2. Here, N is the number of customers in the portfolio/rating grade and D is the number of those customers that have defaulted within that observation period. The p-value (i.e. the cumulative distribution function of the aforementioned beta distribution evaluated at the PD of the portfolio/rating grade) serves as a measure of the adequecy of estimated PD.
