Una versione logit di Merton-Vasicek: A logit version of the models of Merton and Vasicek (Zenodo (CERN European Organization for Nuclear Research))

Summary

• The paper proposes replacing structural asset correlation in the Merton-Vasicek framework with the linear correlation between credit survival logits, enabling the modeling of unlisted corporate credit risk from standard bank rating systems.p.5
• The framework redefines the probability of default as a dynamic hitting probability (PDH) that measures whether the survival logit falls to or below an optimal default threshold h.p.11
• Using long-term historical corporate default data from Moody's spanning 1920 to 2025, survival logit dynamics are tested through Arithmetic Brownian Motion, Ornstein-Uhlenbeck, and Ornstein-Uhlenbeck with jump processes.p.11
• A Monte Carlo simulation across 3,000 scenarios using Banca d'Italia systemic decay rates produced an average default rate of 6.21% and a 99.9% unexpected loss of 7.65% of exposure.p.32

Key insights

1. Survival logit correlations provide a more intuitive and observable alternative to asset correlation across both listed and unlisted corporate credit portfolios.p.5
2. Credit scoring logits capture a broader array of qualitative, balance sheet, and central credit register indicators than traditional market leverage-based Merton models.p.8
3. Dynamic default probability (PDH) reflects the probability that a firm's health state degrades to zero distance-to-default over a specified time horizon rather than acting as a static rating score.p.11
4. Incorporating jump diffusion into Ornstein-Uhlenbeck processes accounts for fat tails and sudden idiosyncratic credit shocks that pure mean-reversion underestimates.p.17
5. Applying the logit Vasicek framework to Moody's aggregate default rates generates unrealistically high stressed default probabilities due to portfolio aggregation distortion.p.26
6. In the metallurgical firm dataset, survival logit correlation averaged 22%, with 78% of pairwise correlation coefficients being positive.p.29
7. Default correlation among the 582 analyzed firms averaged 4.1%, with 85% of correlation pairs falling between 0 and 10%.p.29
8. Calculating regulatory capital requirements as the sum of individual stressed exposures results in 5.76% of total exposure, compared to 11.4% when evaluated directly on aggregate portfolio averages.p.33