Monotonicity of Normalized Implied-Volatility Coordinates under No-Arbitrage

Battle Count: 100

The results are directly relevant to options trading desks and quantitative finance practitioners. The finite-strike monotonicity checks provide simple arbitrage diagnostics for quoted option chains. The model-free variance identity is useful for variance swap pricing and risk management. However, the paper does not propose a trading strategy or provide empirical backtesting. Its primary value is theoretical understanding and practical validation tools for volatility surface construction.

The discrete finite-strike monotonicity checks (Theorems 3.2 and 4.3) are straightforward to implement: verify monotonicity and convexity of quoted call/put prices, check put-call parity, then verify monotonicity of k/v(k) or (F-K)/sigma_N(K). The continuous-strike Fukasawa transformation (Theorem 4.6) and the normal-variance identity (Theorem 5.1) require more sophisticated numerical integration and differentiability assumptions. Overall, the core discrete results are simple; the full framework requires moderate mathematical implementation.

The paper is purely theoretical with self-contained mathematical proofs. All lemmas, theorems, and proofs are fully presented. Verification requires graduate-level mathematical finance knowledge but no external data or code. The discrete finite-strike results are directly checkable against quoted option chains.