The Risk-Neutral Crash Frontier: Sharp Joint Bounds on Crash Probability and Conditional Depth from Option Bid–Ask Quotes

Battle Count: 76

Highly relevant for quantitative trading desks dealing with tail risk, crash insurance, and option-based strategies. The method provides sharp, model-free bounds on crash probability and conditional depth directly from observable bid-ask quotes, enabling: (1) feasible stress scenario validation (checking whether a given probability-depth pair is market-consistent), (2) sharp pricing of digital+put portfolios with dual certificates for hedging, (3) information content analysis of deep OTM put wings, and (4) risk committee decision-making without parametric assumptions. The empirical finding that ~37% of marginal-bound scenarios are jointly infeasible has direct implications for risk model calibration. However, the method is primarily a valuation/bounding tool rather than a predictive model for trading signals.

The core LP formulation is straightforward (finite linear inequalities with cell masses, moments, and threshold atom). However, the full pipeline involves: (1) quote normalization and parity conversion, (2) state-space partitioning at strikes and threshold, (3) feasibility checking and Slater condition verification via auxiliary LP, (4) adaptive hull reconstruction with support programs and edge-gap criteria, (5) polygon-to-depth transformation via change-of-variables, (6) dual certificate extraction and portfolio interpretation, (7) bootstrap inference, and (8) handling of inconsistent cross sections via slack relaxation. The adaptive hull algorithm with numerical tolerances and the transformed area calculation add implementation subtlety. Requires a reliable LP solver (e.g., Gurobi, CPLEX, or open-source alternatives).

The methodology is fully specified with detailed proofs, algorithm descriptions, and parameter settings (tolerances, bootstrap blocks, quote selection rules). However, the primary data source (OptionMetrics SPX bid-ask quotes) is proprietary and not freely available. The paper provides extensive appendix details on sampling rules, tie-breaking, and numerical parameters. No code repository is mentioned. The synthetic validation cases and the adaptive hull algorithm are described in sufficient detail for independent implementation.