Faster Monotone Implied Volatility Solver

Battle Count: 83

Implied volatility inversion is a fundamental operation in options trading, calibration, and risk management. ThiopheneIV offers lower latency than Jäckel's Let's Be Rational on all eight benchmark datasets (167-177ns vs 204-263ns unpolished), making it relevant for high-frequency calibration and real-time risk systems. The monotone convergence guarantee provides mathematical transparency absent from purely empirical methods. However, the accuracy gap vs multiprecision reference without polish (up to 329 ulps) and the dependency on boundary handling for production robustness temper the practical advantage.

The core algorithm (Choi L3 seed + 3 Euler-Chebyshev/Halley steps) is mathematically clean and well-proven. However, production deployment requires extensive boundary handling: parity normalisation, microscopic Bachelier-limit branches, saturated price treatment, Choi seed repair fallbacks, and optional Jäckel-Newton polish. The paper explicitly states that 'robust production inversion still depends on boundary handling and on the pricing objective one chooses to match.' The erfcx dependency requires a high-quality implementation (Apache Commons Numbers recommended).

Source code for benchmark tables, solver variants, benchmark harnesses, and dataset builders is available in the accompanying source distribution. Exact dataset grids are reproduced in Appendix A. The paper provides detailed algorithmic specifications, proofs, and worked examples. However, no explicit public repository URL is given in the text.