An empirical comparative analysis of foreign exchange smile calibration procedures

Dimitri Reiswich

Journal of Computational Finance

Abstract: ABSTRACT Very little is known in the academic literature about the construction of the implied volatility smile in foreign exchange over-the-counter derivative markets. These markets have adapted to foreign exchange-specific quotation mechanisms where the volatility smile is given implicitly, through market quotes, rather than explicitly. The resulting smile setup problem requires a numerical calibration procedure where various interpolation functions can be used.We will introduce different calibration setups and compare them empirically with respect to their computational robustness, well-posedness of the calibration setup, extrapolation behavior and ability to produce volatility smiles consistent with no-arbitrage conditions. We find that the simplified parabolic interpolation is the most suitable calibration method. Finally, we analyze potential smile construction problems in the presence of extreme market scenarios.

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