Common ordinal models, including the ordered logit model and the continuation ratio model, are structured by a common score (i.e., a linear combination of a list of given explanatory variables) plus rank specific intercepts. Sensitivity with respect to the common score is generally not...

Abstract Given a risk outcome y over a rating system {R_i }_(i=1)^k for a portfolio, we show in this paper that the maximum likelihood estimates with monotonic constraints, when y is binary (the Bernoulli likelihood) or takes values in the interval 0≤y≤1 (the quasi-Bernoulli likelihood), are...

Estimation of portfolio expected credit loss is required for IFRS9 regulatory purposes. It starts with the estimation of scenario loss at loan level, and then aggregated and summed up by scenario probability weights to obtain portfolio expected loss. This estimated loss can vary significantly,...

Rating transition models are widely used for credit risk evaluation. It is not uncommon that a time-homogeneous Markov rating migration model deteriorates quickly after projecting repeatedly for a few periods. This is because the time-homogeneous Markov condition is generally not satisfied. For...

We discuss the economic reasons why the predictions of price and return statistical moments in the coming decades, in the best case, will be limited by their averages and volatilities. That limits the accuracy of the forecasts of price and return probabilities by Gaussian distributions. The...

This work proposes a class of seasonal autoregressive integrated moving average models whose period is an independent and identically distributed random process valued in a finite set. The causality, invertibility, and autocovariance shape of the model are first revealed. Then, the estimation of...