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Estimating relative risk aversion, risk-neutral and real-world densities using brazilian real currency options

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

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 risktransformations. 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.

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  • Ornelas, José Renato Haas & Barbachan, José Santiago Fajardo & Farias, Aquiles Rocha de, 2012. "Estimating relative risk aversion, risk-neutral and real-world densities using brazilian real currency options," EBAPE Working Papers 1, FGV EBAPE - Escola Brasileira de Administração Pública e de Empresas (Brazil).
    • Handle: RePEc:fgv:ebapwp:1
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    3. Cavalcanti, T. & Iyer, S. & Rauh, C. & Roerig, C. & Vaziri, M., 2022. "A City of God: Afterlife Beliefs and Job Support in Brazil," Cambridge Working Papers in Economics 2268, Faculty of Economics, University of Cambridge.
    4. Tiago Cavalcanti & Bruno Martins & Cezar Santos & Joseph Kaboski, 2018. "Dispersion in Financing Costs and Development," 2018 Meeting Papers 426, Society for Economic Dynamics.
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    6. Angelo Marsiglia Fasolo, 2012. "A Note on Particle Filters Applied to DSGE Models," Working Papers Series 281, Central Bank of Brazil, Research Department.
    7. Waldyr Areosa & Marta Areosa, 2012. "Information (in) Chains: information transmission through production chains," Working Papers Series 286, Central Bank of Brazil, Research Department.
    8. 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.
    9. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle: survey and outlook," Annals of Finance, Springer, vol. 14(3), pages 289-329, August.
    10. 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, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 71(1), May.
    11. Etelvina Stefani Chavez & Gastón Milanesi & Gabriela Pesce, 2021. "Aversión al riesgo implícita en los precios de mercado de diferentes activos financieros de Argentina," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(1), pages 1-23, Enero - M.
    12. Ornelas, José Renato Haas, 2016. "The Forecast Ability of Option-implied Densities from Emerging Markets Currencies," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 36(1), March.

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