Counterexamples for FX Options Interpolations - Part II

Battle Count: 91

Highly relevant for FX options desks and quantitative researchers working on volatility surface construction. The findings directly impact how traders and quants calibrate implied volatility surfaces from broker quotes, which affects option pricing, hedging (Greeks), and risk management. The counterexamples showing that different interpolation methods yield different vanilla volatilities are practically important for any FX options trading operation. However, it is more relevant to derivatives pricing and risk than to directional trading strategies.

The paper describes multiple calibration algorithms with nested optimization loops, delta lookups requiring numerical solvers, and handling of non-monotonic delta functions. Implementation requires careful numerical methods (Newton's method, bracketing solvers like TOMS748, Gauss-Newton optimizers), handling of edge cases (non-monotonic deltas, unreachable deltas at high vol), and proper weighting schemes (inverse vega weights). The mathematical formulations are clear but translating them into robust production code is non-trivial.

The paper provides specific market data (EUR/HKD, EUR/TRY, USD/JPY, USD/AED, AUD/NZD quotes with dates and parameters), detailed algorithmic steps, and mathematical formulations. However, no code repository is provided. The numerical examples use specific market data that may not be freely available. The methodology is well-described with equations and algorithm steps, making it theoretically reproducible but practically challenging without code.