Faster Monotone Implied Volatility Solver

TL;DR

ThiopheneIV is a novel, efficient implied-volatility solver that combines a monotone core with explicit guards, improving speed and accuracy over existing methods.

Contribution

The paper introduces ThiopheneIV, a new implied-volatility solver with a monotone core and robust boundary handling, offering faster performance and high accuracy.

Findings

ThiopheneIV outperforms Java port of J"ackel's method in speed.

ThiopheneIV maintains low grid errors close to reference prices.

ThiopheneIV+ achieves even closer agreement with expanded reference prices.

Abstract

We present ThiopheneIV, a Black-Scholes implied-volatility solver with a monotone core and explicit production guards. Prices are first reduced to J\"ackel's out-of-the-money normalisation and inverted through a tail-stable logarithmic price equation. The solver starts from the non-iterative Choi-Huh-Su L3 lower-bound seed and applies three Euler-Chebyshev corrections. In exact arithmetic, the seed is below the admissible root and the Euler-Chebyshev map increases monotonically without overshooting; the proof is included. The implementation then adds the floating-point machinery needed in practice: parity normalisation, microscopic Bachelier-limit handling, saturated-price treatment, finite-update checks, fallback seeds, and an optional J\"ackel-Newton polish. Against the highly accurate expanded J\"ackel reference price, ThiopheneIV is faster than a Java port of J\"ackel's Let's Be Rational while keeping regular-grid errors close. ThiopheneIV+ adds one final J\"ackel-Newton correction for systems that need closer agreement with that expanded reference price. The broader lesson is that a convergence proof gives a clean core, but robust production inversion still depends on boundary handling and on the pricing objective one chooses to match.