Multi-Credit Calibration via Elastically Stopped Lévy Processes

Battle Count: 61

Highly relevant for credit derivatives desks and quantitative risk teams. The paper provides an exact, tractable framework for pricing CDS and index tranches that dominates industry-standard benchmarks (Gaussian copula, Duffie-Garleanu). The ability to reproduce inverted spread curves of distressed names is practically valuable for identifying names heading into default. The Wiener-Hopf Monte Carlo scheme offers order-of-magnitude speed improvements over Euler simulation for portfolio pricing. However, the paper focuses on pricing and calibration rather than trading strategy development, and the model complexity may limit real-time implementation without significant engineering effort.

High implementation complexity due to: (1) Lévy process fluctuation theory and scale functions; (2) Phase-type jump representation and polynomial root-finding for the Laplace transform; (3) Talbot contour numerical Laplace inversion with singularity auditing; (4) Wiener-Hopf factorization and exact sampling of supremum-position pairs; (5) Bilevel calibration with coordinate descent over static parameters and per-date state; (6) ISDA-style bootstrap of forward hazard rates from CDS quotes; (7) Tranche pricing via default-count law conversion. The mathematical machinery is well-documented but requires expertise in stochastic processes, numerical analysis, and credit derivatives.

The paper provides complete mathematical derivations, explicit pricing formulas (Theorem 2.3), detailed calibration protocols, and data source descriptions (S&P Global via WRDS, Markit composites, FRED Treasury yields). However, no code repository is provided, and the data requires commercial subscriptions. The Talbot contour inversion parameters (N_theta=18, q=16) and all model specifications are fully documented. The Wiener-Hopf Monte Carlo scheme is described algorithmically but not provided as code.