Faster Monotone Implied Volatility Solver

Fabien Le Floc'h

Papers from arXiv.org

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.

Date: 2026-05
References: Add references at CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2605.22427 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2605.22427

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().