Subjective Probability Density Functions from FX Option Prices: Predictive Power and Performance on a Carry Trade Strategy

In this article, we extracted the risk†neutral densities (RNDs) and subjective probability density functions of the US Dollar/Brazilian Real (USD/BRL) exchange rate and evaluated its performance in predicting the future realizations of the USD/BRL exchange rate. The RNDs were estimated using two structural models and three nonstructural models. In the first category, we included the Variance Gamma†OU model and the CGMY Gamma†OU model. In the second category, we included the density functional based on confluent hypergeometric function model, the mixture of lognormal distributions model, and the smoothed implied volatility smile. The density functional based on confluent hypergeometric function and the CGMY Gamma†OU produced 1†month term densities (RND and subjective probability density function) with the highest forecasting power of the 1†month USD/BRL exchange rate. Finally, we applied the CGMY Gamma†OU model to extract a sample of subjective cumulative probabilities of 1†month USD/BRL movements, and used them as explanatory variables in predictive time series models, whose dependent variable was the 1†month carry trade return. Its predictive power was then tested and confirmed in three trading strategies that over performed the standard carry trade strategy in terms of annualized cumulative returns.