Dynamic model of corporate credit ratings and defaults

This repository contains code and a synthetic data set for reproducing the modeling framework in Vana and Hornik (2020).

Data set

The synthetic data set synthetic_dat.rda has been generated using the synthpop R package (Nowok et. al, 2016) by replacing all observations with values simulated from probability distributions specified to preserve key features of the actual observed data.

The data set contains 19952 rows and 13 columns:

• firm_id: integer containing the firm id, maximum is 2528

• year_id: integer containing the year id, maximum is 19

• R1: integer corresponding to the rating classes assigned by rater 1

• R2: integer corresponding to the rating classes assigned by rater 2

• R3: integer corresponding to the rating classes assigned by rater 3

• D : binary indicator for default

• X1 to X7: standardized covariates.

Models

The Stan codes for the five models introduced in the papers can be found in the Stan folder.

• Model_S1_logit_priors-eps-N_bias-0.stan
• Model_S2_logit_priors-eps-N_bias-diffgammas.stan
• Model_D1_logit_priors-a-HN-b-AR1-eps-AR1_bias-0.stan
• Model_D2_logit_priors-a-HN-b-AR1-eps-AR1_bias-diffgammas.stan
• Model_PM_logit_priors-a-HN-b-AR1-eps-AR1_bias-diffbetas-delta-AR1.stan

Estimation of the models using RStan

Simulation study

In the folder Simulation, the Simulation.Rmd file can be used to reproduce the analysis from the online appendix of the paper.

Synthetic data

In the folder Synthetic_Data, the Synthetic_Data_Analysis.Rmd contains the code for reproducing the analysis in that it performs the out of sample analysis by repeatedly estimating the five models presented in the paper (PM, S1, S2, D1, D2) using the RStan package (Stan Development Team, 2020) for different training vs. test samples from synthetic_dat.rda. In the one-step-ahead prediction exercise we train the model on data containing years 1 to t and then evaluate the log predictive likelihoods for the following year t + 1. We illustrate the approach for $t = 13,\ldots, 19$.

The code creates a folder Results_Synthetic_Data which contains resulting .rda files for each test period. Code for computing the out-of-time measures is provided.

References

Beata Nowok, Gillian M. Raab, Chris Dibben (2016). synthpop: Bespoke Creation of Synthetic Data in R. Journal of Statistical Software, 74(11), 1-26. doi:10.18637/jss.v074.i11

Stan Development Team (2020). RStan: the R interface to Stan. R package version 2.19.3. http://mc-stan.org/.