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

12 Pages Posted: 21 Sep 2011

See all articles by Jose Renato Haas Ornelas

Jose Renato Haas Ornelas

Banco Central do Brasil

José Fajardo

Getulio Vargas Foundation

Aquiles Farias

Government of the Federative Republic of Brazil - Central Bank of Brazil

Date Written: September 20, 2011

Abstract

Building Risk-Neutral Densities (RND) from options data can provide market-implied expectations about the future behavior of a financial variable. And market expectations on financial variables may influence macroeconomic policy decisions. It can be useful also for corporate 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/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 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 real-world density 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 relative risk aversion parameter is around 2.7, which is in line with other articles that have estimated this 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 to forecast the Brazilian Real exchange rate. Abe et all (2007) found also mixed results 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-world density, the out-of-sample performance improves substantially, with satisfactory results in both 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 Real exchange rate.

Keywords: Risk-Neutral Densities, Relative Risk Aversion, Currency Options

JEL Classification: C13, C16, E47, E52, G12, G13, G17

Suggested Citation

Ornelas, Jose Renato Haas and Fajardo, José and Farias, Aquiles, Estimating Relative Risk Aversion, Risk-Neutral and Real-World Densities Using Brazilian Real Currency Options (September 20, 2011). Available at SSRN: https://ssrn.com/abstract=1931388 or http://dx.doi.org/10.2139/ssrn.1931388

Jose Renato Haas Ornelas (Contact Author)

Banco Central do Brasil ( email )

P.O. Box 08670
SBS Quadra 3 Bloco B - Edificio-Sede
Brasilia, Distrito Federal 70074-900
Brazil

HOME PAGE: http://www.bcb.gov.br

José Fajardo

Getulio Vargas Foundation ( email )

Brazil
55213799 5781 (Phone)

HOME PAGE: http://www.josefajardo.com

Aquiles Farias

Government of the Federative Republic of Brazil - Central Bank of Brazil ( email )

P.O. Box 08670
SBS Quadra 3 Bloco B - Edificio-Sede
Brasilia DF 70074-900, Distr. Federal 70074-900
Brazil

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