Volatility Smile and Risk Neutral Density for FX Options : An Example for the USDMXN

This paper provides a number of relevant guidelines to build a consistent Volatility Smile accounting for the FX market conventions. This consistency is understood as fitting a model which is able to price vanilla options across all possible strikes given the knowledge of a few market structures. To that end, the following models are introduced: Vanna-Volga, SABR, and a Quadratic Polynomial. In addition, the Risk Neutral Density is estimated with the first two models. It is shown that not accounting for such conventions can lead to signicant errors in the estimations.These methods can find important applications in risk management, portfolio selection, and financial event studies