Counterexamples for FX Options Interpolations – Part I

ArXiv ID: 2512.19621 “View on arXiv”

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.

Keywords: FX Options, Volatility Interpolation, Local Volatility, Stochastic Volatility, Risk Management, Foreign Exchange (FX)

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: 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.

  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"]