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

The objective of this paper is to provide the main guidelines to correctly handle the FX market conventions in order to build a consistent Volatility Smile. The models detailed for the Volatility Smile are: Vanna Volga, SABR and a Quadratic Polynomial in Delta. Hopefully, further research can incorporate these models instead of the one introduced by Malz. Also, it is shown how to estimate the Risk Neutral Density for the Vanna Volga and SABR models, which can be used for risk assessment or even to analyze monetary policy or interventions in the FX market.