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   "estimand": "Model-implied CDX and CDX tranche spreads (levels and time series) compared with observed spreads",
   "strategy": "Calibrate an equilibrium rare-disaster model to consumption data and the equity premium. Extract latent state variables from index option implied volatilities. Compare predicted tranche spreads with data and run comparative statics.",
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    "Time-varying disaster probability governed by square-root processes",
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    "Preference and consumption parameters taken from prior studies without reference to CDX data"
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    "Disaster risk is linked tightly to the equity premium, so a low-equity-premium recalibration fails",
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   "convention_notes": "Tables report calibrated parameters and data-versus-model moments. Simulated small-sample percentiles (5th, 50th, 95th) are shown alongside population moments. Tranche spreads are given in basis points per year, with the equity tranche reported as an upfront payment. Pre-crisis and crisis subsamples are reported separately.",
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    "claim": "Calibrated disaster model matches average five- and three-year CDX tranche spreads before and during the crisis",
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    "claim": "Model reproduces the time series of tranche spreads using option-implied state variables",
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   {
    "claim": "Lower equity premium calibration produces senior tranche spreads far below the data",
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    "evidence_ref": "Figure 9"
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    "claim": "Model matches physical default probabilities across horizons",
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    "claim": "Model cannot reconcile low implied-volatility autocorrelation with a persistent price-dividend ratio",
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    "evidence_ref": "Figure 10, Table IV"
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    "claim": "Model predicts counterfactually low long-term real bond yields",
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    "evidence_ref": "Figure 11"
   },
   {
    "claim": "Model matches equity premium and bill rate moments",
    "evidence_type": "table",
    "evidence_ref": "Table II"
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  "structural_summary": "The paper motivates the question with dramatic crisis-era senior tranche pricing and a gap: few quantitative models link structured products to fundamentals. It then positions itself against no-arbitrage models, whose limitation is incomplete markets, and turns to an equilibrium model. Next it sketches the mechanism tying the equity premium to tranche prices. A theory section presents a continuous-time disaster model, followed by data, calibration (including option-based extraction of state variables), and an evaluation of averages, time series and comparative statics. It then examines implications for options, the price-dividend ratio and bonds, honestly reporting where the model fails. The conclusion restates the fit and lists remaining puzzles.",
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