Counterexamples for FX Options Interpolations - Part I

Battle Count: 72

Highly relevant for FX options desks, structured product desks, and risk management teams. The paper directly impacts pricing and hedging of vanilla FX options, digital options, auto-quanto options, and variance swaps. Understanding interpolation failures is critical for accurate Greeks computation (especially Gamma), model calibration, and avoiding mispricing in exotic derivatives valued with local volatility models. The findings on flat wings and their impact on long-dated derivatives are practically significant.

The counterexample analysis itself is straightforward (fitting known parameterizations to given quotes). However, implementing the various interpolation schemes correctly requires: solving non-linear equations for delta-based lookups (Newton/Brent methods), computing Dupire local variance denominators, handling spline boundary conditions, implementing SVI/SABR/xSSVI/LVG calibrations, and performing dense-grid replication for variance swaps and auto-quanto options. The numerical methods (fixed-point convergence issues) add complexity.

The paper provides detailed market data (Tables 1-7) with specific dates, forwards, rates, and quotes. Calibration procedures are referenced (De Marco and Martini 2009 for SVI, Corbetta et al. 2019 for xSSVI). However, no code or repository is provided, and some data (e.g., EUR/CZK 5Δ quotes) may require access to market data providers like Reuters or SuperDerivatives.