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

Jose Ornelas, José Fajardo (pepefb@gmail.com) and Aquiles de Farias (aquiles.farias@gmail.com)

No 269, Working Papers Series from Central Bank of Brazil, Research Department

Abstract: Building Risk-Neutral Densities (RND) from options data can provide market-implied expectations about the future behavior of a financial variable. This paper uses the Liu et all (2007) approach to estimate the option-implied risk-neutral densities from the Brazilian Real/US Dollar exchange rate distribution. We then compare the RND with actual exchange rates, on a monthly basis, in order to estimate the relative risk-aversion of investors and also obtain a real-world density for the exchange rate. We are the first to calculate relative risk-aversion and the option-implied real world Density for an emerging market currency. Our empirical application uses a sample of exchange-traded Brazilian Real currency options from 1999 to 2011. The RND is estimated using a Mixture of Two Log-Normals distribution and then the real-world density is obtained by means of the Liu et al. (2007) parametric risk-transformations. Our estimated value of the relative risk aversion parameter is around 2.7, which is in line with other articles that have estimated this parameter for the Brazilian Economy. Our out-of-sample evaluation results showed that the RND has some ability to forecast the Brazilian Real exchange rate. However, when we incorporate the risk aversion into RND in order to obtain a Real-world density, the outof- sample performance improves substantially. Therefore, we would suggest not using the “pure” RND, but rather taking into account risk aversion in order to forecast the Brazilian Real exchange rate.

Date: 2012-03
New Economics Papers: this item is included in nep-cfn and nep-for
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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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