RESEARCH · GLOBAL
Proof of monotonicity in normalized implied-volatility coordinates under no-arbitrage
Theoretical result: for a fixed option maturity, arbitrage-free option smiles induce natural normalized strike coordinates with proven monotonicity properties. Supports calibration of option-pricing models without edge-case violations.
WHY IT MATTERS
Options traders and risk managers calibrating stochastic volatility models now have a pure-math guarantee that normalized coords respect no-arbitrage—simplifies model fitting and reduces exotic smile artefacts.
Source: arXiv · 2026-06-24