Robust Volatility Index Calculation with OTM Option-implied Probability

Battle Count: 73

Highly relevant to quantitative trading. Volatility indices (especially VIX) are fundamental inputs for volatility trading strategies, options market making, risk management, and portfolio hedging. The paper directly addresses the robustness of volatility estimation during market stress (e.g., COVID-19 crash), which is precisely when accurate risk measurement is most critical for trading decisions. The method's ability to handle illiquid markets and zero-bid scenarios makes it practically valuable for real-time trading systems. However, it is more of a measurement/estimation tool than a direct trading signal generator.

The mathematical construction is elegant but involves multiple geometric steps: identifying valid linear functions from pairs of ask prices, filtering by slope and intercept conditions, computing indices IL/IM and JL/JM, constructing auxiliary functions f0 and fD, and taking the supremum. The O(N^2) pair enumeration and filtering logic requires careful implementation. Handling edge cases (L=∅, M=∅, arbitrage-violating data) adds complexity. The actual integration for volatility computation is straightforward once the price function is constructed. No reference implementation is provided.

The mathematical methodology is fully specified with proofs and algorithms. However, the empirical analysis relies on the commercial OptionMetrics IvyDB database, which is not freely available. The VIX benchmark calculation follows the Cboe White Paper methodology. No code or repository is provided. The geometric construction algorithm is described in sufficient detail for reimplementation, but practical implementation details (e.g., handling edge cases, numerical precision) are not fully specified.