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Recovering Risk-Neutral Densities from Brazilian Interest Rate Options

José Renato Haas Ornelas, Marcelo Yoshio Takami


Building Risk-Neutral Density (RND) from options data is one useful way for extracting market expectations about a financial variable. For a sample of IDI (Brazilian Interbank Deposit Rate Index) options from 1998 to 2009, this paper estimates the option-implied Risk-Neutral Densities for the Brazilian short rate using three methods: Shimko, Mixture of Two Log-Normals and Generalized Beta of Second Kind. Our in-sample goodness-of-fit evaluation shows that the Mixture of Log-Normals method provides better fitting to option’s data than the other two methods. The shape of log-normal distributions seems to fit well to the mean-reversal dynamics of Brazilian interest rates. We have also calculated the RND implied Skewness, showing how it could have provided market early-warning signals of the monetary policy outcomes in 2002 and 2003. Overall, Risk-Neutral Densities implied on IDI options showed to be a useful tool for extracting market expectations about future outcomes of the monetary policy.


Risk-Neutral Density, Interest Rate Options, Generalized Beta, Mixture of Log-Normals

RBFin - Brazilian Review of Finance, rbfin@fgv.br, (+55-21) 2598-9800
A publication of the Brazilian Society of Finance