New Paper Gives Exact Pricing and Analytic Risk Attribution for First-to-Default Basket Swaps

DrCirillo · x · 2026-10-13

Pasquale Cirillo of ZHAW released a corrected, extended paper on first-to-default (FtD) basket swaps with heterogeneous recoveries.

• Building on an algebraic framework for extremal stability, it identifies a broad class of default models where the first defaulter follows a softmax law and default timing is independent of default identity
• Within this class, protection value factorizes into severity and timing terms, a single name-level attribution works for every contract, and all hazard/recovery sensitivities are analytic
• It shows contract-independent attribution exists iff identity and timing are independent — not mutual independence of defaults — holding exactly under common frailty, Marshall–Olkin shocks, and differentiable extreme-value survival copulas
• A piecewise extension gives exact tenor calibration, with an application to public CDS quotes showing the assumptions are milder than they appear

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