Estimating Relative Risk Aversion, Risk-Neutral and Real-World Densities using Brazilian Real Currency Options

Jose Renato Haas Ornelas (), José Fajardo () and Aquiles Rocha de Farias ()

No 1, EBAPE Working Papers from School of Public and Business Administration, Getulio Vargas Foundation (Brazil)

Abstract: Building Risk-Neutral Densities (RND) from options data can provide market-impliedexpectations about the future behavior of a financial variable. And market expectations onfinancial variables may influence macroeconomic policy decisions. It can be useful also forcorporate and financial institutions decision making. This paper uses the Liu et all (2007)approach to estimate the option-implied Risk-neutral densities from the Brazilian Real/USDollar exchange rate distribution. We then compare the RND with actual exchange rates, ona monthly basis, in order to estimate the relative risk-aversion of investors and also obtain aReal-world density for the exchange rate. We are the first to calculate relative risk-aversionand the option-implied Real World Density for an emerging market currency. Our empiricalapplication uses a sample of Brazilian Real/US Dollar options traded at BM&F-Bovespafrom 1999 to 2011. The RND is estimated using a Mixture of Two Log-Normals distributionand then the real-world density is obtained by means of the Liu et al. (2007) parametric risktransformations.The relative risk aversion is calculated for the full sample. Our estimatedvalue of the relative risk aversion parameter is around 2.7, which is in line with other articlesthat have estimated this parameter for the Brazilian Economy, such as Araújo (2005) andIssler and Piqueira (2000). Our out-of-sample evaluation results showed that the RND hassome ability to forecast the Brazilian Real exchange rate. Abe et all (2007) found also mixedresults in the out-of-sample analysis of the RND forecast ability for exchange rate options.However, when we incorporate the risk aversion into RND in order to obtain a Real-worlddensity, the out-of-sample performance improves substantially, with satisfactory results inboth Kolmogorov and Berkowitz tests. Therefore, we would suggest not using the “pure”RND, but rather taking into account risk aversion in order to forecast the Brazilian Realexchange rate.

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Date: 2012-04-12
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Working Paper: Estimating Relative Risk Aversion, Risk-Neutral and Real-World Densities using Brazilian Real Currency Options (2012)
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