Common use of Model Selection Clause in Contracts

Model Selection. In order to compare our dynamic latent trait model with the benchmark model we use the deviance information criterion (DIC; according to ▇▇▇▇▇▇▇▇▇▇▇▇▇ et al., 2002). The DIC is a generalization of the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) for hierarchical models. In contrast to the AIC and BIC, DIC allows to compare Bayesian hierarchical models where the effective number of parame- ters is not clearly defined. Similar to the other information criteria a trade-off between model fit and model complexity is evaluated. The DIC contains one penalty term for the effective number of parameters used measuring model complexity and one term equal to the deviance of the likelihood measuring model fit. A lower DIC value indicates a better model fit. According to ▇▇▇▇▇▇▇▇▇▇▇▇▇ et al. (2002), if the difference in DIC is greater than 10, then the model with the larger DIC value has considerably less support than the model with the lower DIC value. For our models, the lower DIC value of our dynamic latent trait model (DIC = 9485.77) indicates that this model dominates in the terms of model fit as well as model complexity the obvious benchmark model (DIC = 12319.82). Rating errors. We begin our analysis of the estimation results with the rating errors. Our dynamic latent trait model captures estimates for the rating bias µj and the standard deviation σj of the rating error of the big three external rating agencies on the score scale. Table 3.8 shows the results for the estimated posterior distribution of the parameters for the three raters µj and σj, respectively. The posterior distributions of the parameters are characterized by the mean values (mean) and the standard deviations (SD) of the 18, 000 (4 × 4, 500) posterior draws. We infer from Table 3.8 that Fitch has the smallest absolute rating bias from µj σj mean SD mean SD Fitch 0.0155 0.0018 0.0752 0.0021 Moody’s 0.0887 0.0024 0.1013 0.0029 S&P 0.0732 0.0017 0.0641 0.0017 Table 3.8: Estimated rating bias µj and standard deviations σj for the rat- ing errors (on the score scale) of the big three external rating agencies Fitch, Moody’s and Standard&Poor’s. The posterior distributions of the parame- ters are characterized by the mean values (mean) and the standard deviations (SD) of the 18, 000 (4 × 4, 500) posterior draws. the consensus on the score scale with respect to the posterior mean (0.0155). Moody’s clearly seems to be too optimistic in its credit assessment yielding a posterior mean for the rating bias µ of −0.089 on the score scale. Note, that our model is based on the thresholds λj,k (and therefore PD equivalents) which are clearly lower for Moody’s than the other two raters. Despite the high difference (on the score scale: 0.139) in the PD equivalents of Moody’s and Standard&Poor’s indicated in the Appendix (see Figure 3.5), Moody’s is still more optimistic by rating investment-grade firms than Standard&Poor’s. In this study, ▇▇▇▇▇▇▇&▇▇▇▇’▇ is with a posterior mean of the rating bias of 0.073 the most conservative rater out of the three considered rating agencies. In addition to the rating biases, our model captures the standard deviation (precision) of the rating errors of the three raters (Table 3.8). Whereas the posterior mean of the standard deviation σ of the rating errors is rather similar for Fitch and Standard&Poor’s (0.075, 0.064), Moody’s has a higher posterior mean of the standard deviation (0.101), indicating that its ratings deviate more strongly from the consensus ratings. Consensus score. In addition to the analysis of the bias/variance struc- ture of the rating errors, we analyze the estimated consensus scores of our dynamic latent trait model. Instead of showing the consensus scores of all iTraxx Europe companies, Figure 3.6 shows the estimated consensus rating scores of four sample companies (ENELSPA, NESTLE, GLENCORE INT. AG, ROYAL BANK OF SCOTLAND) and compares them with the original ratings (mapped onto the score scale) of the three raters Fitch, Moody’s and Standard&Poor’s as well as with the mean rating score of the three raters.