Multi-Credit Calibration via Elastically Stopped Lévy Processes

2026-08-10

AI Summary

This study addresses the accurate calibration of default risk and dependence among multiple obligors—particularly tail risk and simultaneous defaults—by introducing a novel framework based on elastic-stopping Lévy processes, which preserves the interpretability of structural models. Default occurs when a spectrally positive stress process crosses an exponential barrier, with synchronous defaults captured through a common compound Poisson jump component. The authors innovatively combine a Cox construction with phase-type jumps to derive, for the first time, a finite partial-fraction representation of the Laplace transform of default probabilities, enabling analytical tractability and reproducing inverted credit spread curves. Efficient pricing is achieved via Wiener–Hopf Monte Carlo methods, yielding the lowest out-of-sample errors on CDX North America high-yield and investment-grade tranches. The single-factor structure closes 73%–89% of the tranche pricing gap, rising to 95% after rescaling, significantly outperforming both Gaussian copula and Duffie–Gârleanu affine intensity models.

Abstract

We calibrate credit default swaps and index tranches with elastically stopped Lévy processes: each firm defaults when the running supremum of a latent, spectrally positive distress process crosses an independent exponential barrier. This yields a Cox construction with totally inaccessible default times, while retaining the interpretability and explicit formulas of a structural approach. Adding a single common compound Poisson jump factor to every firm's latent driver gives a parsimonious multi-credit model with simultaneous defaults, which is priced by an exact Wiener--Hopf Monte Carlo scheme. Its tractability rests on a single-name result we prove: a finite partial-fraction formula for the Laplace transform of the default probability under phase-type jumps. On daily CDX North American High-Yield and Investment-Grade panels, our drivers attain the lowest out-of-sample errors in a six-model field and reproduce the inverted spread curves of names heading into default, which a Lévy subordinator provably does not. At the index level, the two-parameter dependence structure closes $73\%$ to $89\%$ of the tranche pricing gap left by independent marginals with the dependence parameters frozen, and up to $95\%$ once re-marked to tranche quotes; our framework dominates a single-factor Gaussian copula and the affine intensity benchmark of Duffie--Gârleanu on both indices.

Problem

• multi-credit calibration
• credit default swaps
• simultaneous defaults
• tranche pricing
• default time modeling

Innovation

• elastically stopped Lévy processes
• multi-credit calibration
• simultaneous defaults
• Wiener–Hopf Monte Carlo
• phase-type jumps