An empirical comparative analysis of foreign exchange smile calibration procedures

Dimitri Reiswich

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.