Paper: arXiv 2512.19621

Authors: Jherek Healy

Abstract

This article provides a list of counterexamples, where some of the popular fx option interpolations break down. Interpolation of FX option prices (or equivalently volatilities), is key to risk-manage not only vanilla FX option books, but also more exotic derivatives which are typically valued with local volatility or local stochastic volatilility models.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical derivations (e.g., local variance denominator, SVI parameterization, spline theory) but is heavily grounded in real-world market data and implementation issues, with specific numerical examples, calibration procedures, and direct backtesting implications for FX options interpolation.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Identify breakdown cases in<br>FX Options Interpolation"] --> B["Methodology:<br>Analyze popular interpolation<br>techniques (Vol & Price)"]
  B --> C["Data/Inputs:<br>Selected FX option market data<br>with specific volatility smiles"]
  C --> D["Computational Process:<br>Apply interpolations & test for<br>arbitrage (e.g. negative vol/cdf >1)"]
  D --> E["Key Findings:<br>Counterexamples found where<br>interpolations produce arbitrage,<br>impacting Local Vol/SLV models"]

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1 of 58 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.