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

Informações

Código: FIN797
Divisão: FIN - Finanças
Tema de Interesse: Tema 03 - Gestão de Riscos e Derivativos

Autores

José Renato Haas Ornelas, Aquiles Rocha de Farias, José Santiago Fajardo Barbachan

Resumo

Building Risk-Neutral Densities (RND) from options data can provide market expectationsabout the future behavior of a financial variable. And market expectations on financialvariables may influence macroeconomic policy decisions. It can be useful also for corporateand financial institutions decision making. The articles of Shimko (1993), Rubinstein (1994)and Jackwerth and Rubistein (1996) were the first to empirically obtain RND. It is alsopossible to estimate the relative risk aversion from option prices, as done by Jackwerth (2000)and Bliss and Panigirtzoglou (2004). Most of the works that have studied relative riskaversion estimation have used options on stocks. But, as pointed out by Mico (2005) andBakshi, Carr and Wu (2008), it is important to address the same estimation using currencyoption data in order to obtain a global risk premium. Having the RND and relative riskaversion, one can build a Real-World Density as it is done by Liu et all (2007) usingparametric distributions. This paper uses the Liu et all (2007) approach to estimate theoption-implied Risk-neutral densities from the Brazilian Real/US Dollar exchange ratedistribution. We then compare the RND with actual exchange rates, on a monthly basis, inorder to estimate the relative risk-aversion of investors and also obtain a Real-world densityfor the exchange rate. We are the first to calculate relative risk-aversion and the optionimpliedReal World Density for an emerging market currency. Our empirical application usesa sample of Brazilian Real/US Dollar options traded at BM&F-Bovespa from 1999 to 2011.The RND is estimated using a Mixture of Two Log-Normals distribution and then the realworlddensity is obtained by means of the Liu et al. (2007) parametric risk-transformations.The relative risk aversion is calculated for the full sample. Our estimated value of the relativerisk aversion parameter is around 2.7, which is in line with other articles that have estimatedthis parameter for the Brazilian Economy, such as Araújo (2005) and Issler and Piqueira(2000). Our out-of-sample evaluation results showed that the RND has some ability toforecast the Brazilian Real exchange rate. Abe et all (2007) found also mixed results in theout-of-sample analysis of the RND forecast ability for exchange rate options. However, whenwe incorporate the risk aversion into RND in order to obtain a Real-world density, the out-ofsampleperformance improves substantially, with satisfactory results in both Kolmogorov andBerkowitz tests. Therefore, we would suggest not using the “pure” RND, but rather takinginto account risk aversion in order to forecast the Brazilian Real exchange rate.

Abrir PDF