{"ID":2867231,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.19151","arxiv_id":"2509.19151","title":"Sharp Large Deviations and Gibbs Conditioning for Threshold Models in Portfolio Credit Risk","abstract":"We obtain sharp large deviation estimates for exceedance probabilities in dependent triangular array threshold models with a diverging number of latent factors. The prefactors quantify how latent-factor dependence and tail geometry enter at leading order, yielding three regimes: Gaussian or exponential-power tails produce polylogarithmic refinements of the Bahadur-Rao $n^{-1/2}$ law; regularly varying tails yield index-driven polynomial scaling; and bounded-support (endpoint) cases lead to an $n^{-3/2}$ prefactor. We derive these results through Laplace-Olver asymptotics for exponential integrals and conditional Bahadur-Rao estimates for the triangular arrays. Using these estimates, we establish a Gibbs conditioning principle in total variation: conditioned on a large exceedance event, the default indicators become asymptotically i.i.d., and the loss-given-default distribution is exponentially tilted (with the boundary case handled by an endpoint analysis). As illustrations, we obtain second-order approximations for Value-at-Risk and Expected Shortfall, clarifying when portfolios operate in the genuine large-deviation regime. The results provide a transferable set of techniques-localization, curvature, and tilt identification-for sharp rare-event analysis in dependent threshold systems.","short_abstract":"We obtain sharp large deviation estimates for exceedance probabilities in dependent triangular array threshold models with a diverging number of latent factors. The prefactors quantify how latent-factor dependence and tail geometry enter at leading order, yielding three regimes: Gaussian or exponential-power tails prod...","url_abs":"https://arxiv.org/abs/2509.19151","url_pdf":"https://arxiv.org/pdf/2509.19151v2","authors":"[\"Fengnan Deng\",\"Anand N. Vidyashankar\",\"Jeffrey F. Collamore\"]","published":"2025-09-23T15:30:09Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.ST\",\"q-fin.MF\",\"q-fin.PM\",\"q-fin.RM\"]","methods":"[]","has_code":false}