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

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

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.

Suggested Citation

  • José Renato Haas Ornelas & José Santiago Fajardo Barbachan & Aquiles Rocha de Farias, 2012. "Estimating Relative Risk Aversion, Risk-Neutral and Real-World Densities using Brazilian Real Currency Options," Working Papers Series 269, Central Bank of Brazil, Research Department.
  • Handle: RePEc:bcb:wpaper:269
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    Cited by:

    1. José Renato Haas Ornelas, 2014. "Assessing the Forecast Ability of Risk-Neutral Densities and Real-World Densities from Emerging Markets Currencies," Working Papers Series 370, Central Bank of Brazil, Research Department.
    2. repec:sbe:breart:v:36:y:2016:i:1:a:45406 is not listed on IDEAS
    3. Bruno Martins, 2012. "Local Market Structure and Bank Competition: evidence from the Brazilian auto loan market," Working Papers Series 299, Central Bank of Brazil, Research Department.
    4. Angelo Marsiglia Fasolo, 2012. "A Note on Particle Filters Applied to DSGE Models," Working Papers Series 281, Central Bank of Brazil, Research Department.
    5. Ivanova, Vesela & Puigvert Gutiérrez, Josep Maria, 2014. "Interest rate forecasts, state price densities and risk premium from Euribor options," Journal of Banking & Finance, Elsevier, vol. 48(C), pages 210-223.
    6. repec:fgv:epgrbe:v:71:y:2017:i:1:a:59368 is not listed on IDEAS
    7. Astorino, Eduardo & Chague, Fernando & Giovannetti, Bruno Cara & da Silva, Marcos Eugênio, 2017. "Variance Premium and Implied Volatility in a Low-Liquidity Option Market," Revista Brasileira de Economia - RBE, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 71(1), May.
    8. Waldyr Areosa & Marta Areosa, 2012. "Information (in) Chains: information transmission through production chains," Working Papers Series 286, Central Bank of Brazil, Research Department.

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