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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.

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  • 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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    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. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle: survey and outlook," Annals of Finance, Springer, vol. 14(3), pages 289-329, August.
    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, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 71(1), May.
    8. 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.
    9. 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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