🤖 AI Summary
Long-term default counts often exhibit overdispersion, autocorrelation, and scale-dependent default correlation, which are frequently misattributed to contagion or asset dependence. This work proposes a temporal coarse-graining approach within an Ornstein–Uhlenbeck-driven latent intensity and binomial observation framework (OU–binomial), wherein aggregating default probability paths yields a scale-consistent effective mixture distribution that naturally accounts for these statistical features. This mechanism serves as a benchmark that mitigates overattribution to effects such as Davis–Lo contagion or Vasicek common factors, thereby enhancing model identifiability and predictive consistency. Under controlled residual covariance contributions, the method significantly outperforms direct scale-wise fitting, achieving markedly higher block-wise expected log predictive density.
📝 Abstract
We show that persistent dynamics of a latent default-probability path can generate effective default correlation through temporal coarse-graining. In the OU--Binomial baseline, monthly defaults are conditionally independent given this latent path, but aggregating monthly default probabilities into long-horizon probabilities induces a scale-dependent effective mixing distribution for aggregated default counts. Applied to corporate default-count data, this mechanism explains long-horizon overdispersion, autocorrelation, and the emergence of effective default correlation. We then examine Davis--Lo-type contagion and Vasicek-type common-factor extensions. Direct fitting at each aggregation scale assigns increasing residual covariance shares to instantaneous dependence, but worsens the per-block expected log predictive density. In contrast, when monthly posterior latent paths are first coarse-grained and residual-dependence parameters are estimated conditional on these paths, the residual covariance contributions remain small while the predictive density improves. Thus, temporal coarse-graining provides a scale-consistent baseline that regularizes the attribution of variance and improves identifiability by suppressing the over-allocation of long-horizon fluctuations to contagion or asset-correlation parameters.