Parametric vs. Non-Parametric Methods for Estimating Option Implied Risk-Neutral Densities : The Case of the Exchange Rate Mexican Peso-US Dollar and Mexican Interest Rates

This research paper presents statistical comparisons between two methods that are commonly used to estimate option implied Risk-Neutral Densities (RND). These are: 1) mixture of lognormals (MXL); and, 2) volatility function technique (VFT). The former is a parametric method whilst the latter is a non-parametric approach. The RNDs are extracted from over-the-counter options on the Mexican Peso - US Dollar exchange rate and Mexican interest rates. According to the results the parametric method provided superior in-sample goodness-of-fit for interest rates, which is measured in terms of mean squared errors. For exchange rates both methods were statistically equal. The non-parametric method was the superior one in the out-of-sample evaluations for both financial assets. The implied mean, median and mode were, in general, statistically different between the competing approaches. It is recommended to apply the VFT instead of the MXL given that the former has superior accuracy and it can be estimated when there is a relatively short cross-section of option exercise price range. The results have implications for financial investors and policy makers, especially Central Banks, given that they could use the information content in options to analyze market's perceptions about the future expected variability of the financial assets under study