The Physical Crash Frontier: What Finite Option Quotes Can and Cannot Reveal

Battle Count: 74

Directly relevant to quantitative trading through: (1) model-free crash risk measurement from option prices without parametric assumptions, (2) identification of feasible crash scenarios for stress testing and position sizing, (3) understanding what option quotes can and cannot reveal about tail risk, (4) the finding that puts near the threshold carry most information (80% reduction from 6 nearby puts) guides option data selection for risk models, (5) the tail dilution result warns against overconfidence in crash probability estimates without tail assumptions.

Requires solving finite SOCPs for each direction on a grid (up to 128 directions), constructing cell partitions from strikes, implementing truncated moment conditions (2x2 PSD constraints as SOCP), handling threshold atoms, and performing adaptive grid refinement. The Charnes-Cooper transformation and moment cone construction are non-trivial. Block bootstrap inference adds computational cost. However, standard SOCP solvers (MOSEK, ECOS, SCS) handle the core optimization.

The paper provides complete mathematical formulations, explicit SOCP programs, verification procedures for the regularity condition (99.5-99.8% pass rate), and detailed data construction from OptionMetrics. However, OptionMetrics data is commercially licensed. The adaptive grid construction and all program specifications are fully described. No code repository is mentioned.