Paper: arXiv 2602.12770

Authors: Dohyun Ahn, Agostino Capponi

Abstract

Valuing corporate bonds in systemic economies is challenging due to intricate webs of inter-institutional exposures. When a bank defaults, cascading losses propagate through the network, with payments determined by a system of fixed-point equations lacking closed-form solutions. Standard Monte Carlo methods cannot capture rare yet critical default events, while existing rare-event simulation techniques fail to account for higher-order network effects and scale poorly with network size. To overcome these challenges, we propose a novel approach – Bi-Level Importance Sampling with Splitting – and characterize individual bank defaults by decoupling them from the network’s complex fixed-point dynamics. This separation enables a two-stage estimation process that directly generates samples from the banks’ default events. We demonstrate theoretically that the method is both scalable and asymptotically optimal, and validate its effectiveness through numerical studies on empirically observed networks.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a highly rigorous mathematical approach to a novel problem in quant finance: valuation of corporate bonds subject to systemic network risk. It introduces an innovative Bi-Level Importance Sampling with Splitting (BLISS) method, proving asymptotic optimality while grounding the empirical validation in EBA network data.

Research Flowchart

  flowchart TD
    A["Research Goal: Efficient Valuation of Corporate Bonds in Financial Default Networks"] --> B["Inputs: Network Inter-Institutional Exposures & Asset Value Dynamics"]
    B --> C["Decoupling Strategy: Separate Individual Bank Defaults from Fixed-Point Network Dynamics"]
    C --> D["Bi-Level Importance Sampling: Stage 1 Promotes Default Events Direct Sampling"]
    D --> E["Splitting Technique: Stage 2 Simulates Cascade Losses & Higher-Order Network Effects"]
    E --> F["Validation: Theoretical Proofs & Numerical Simulations on Empirical Networks"]
    F --> G["Outcomes: Scalable, Asymptotically Optimal Method Capturing Systemic Risk"]

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