Eatimating risk aversion, Risk-Neutral and Real-World Densities using Brasilian Real currency options

Abstract

This paper uses the Liu et al. (2007) approach to estimate the optionimplied Risk-Neutral Densities (RND), real-world density (RWD), and relative risk aversion from the Brazilian Real/US Dollar exchange rate distribution. Our empirical application uses a sample of exchange-traded Brazilian Real currency options from 1999 to 2011. Our estimated value of the relative risk aversion is around 2.7, which is in line with other articles for the Brazilian Economy. Our out-of-sample results showed that the RND has some ability to forecast the Brazilian Real exchange rate, but when we incorporate the risk aversion, the out-of-sample performance improves substantially.

Dispersion in Financing Costs and Development

“…The two assigned values are the inverse intertemporal elasticity of substitution parameter, σ = 1.5, and the depreciation rate, δ = 0.06. The intertemporal elasticity is in line with most of the literature on consumption surveyed by Attanasio and Weber (2010) and also with the Brazil-specific literature that estimates σ in the range from 1 to 3 (e.g., Gandelman and Hernández-Murillo, 2014;Fajardo, Ornelas, and Farias, 2012). The depreciation rate is commonly used in the macro growth literature.…”

A Termination Rule for Pension Guarantee Funds

“…The relationship between the optimal termination ratio and the degree of risk aversion characterizing pension beneficiaries is of particular interest. Therefore, relative risk aversion varies between 0 and 5, in keeping with empirically estimated values (see, e.g., Szpiro, ; Jackwerth, ; Chetty, ; Fajardo, Ornelas and De Farias, ). The parameter values employed are summarized in Table .…”

Variance Premium and Implied Volatility in a Low-Liquidity Option Market

“…For instance, Fajardo, Ornelas, & Farias (2012) using data on currency options for the Brazilian Real from 1999 to 2011, estimate the implied riskneutral density and, by comparing it to the objective density, find a coefficient of relative risk aversion of around 2.7. Similarly, Issler & Piqueira (2000) using data on aggregate consumption from 1975 to 1994, 14 We use their simpler equation, where they assume a constant volatility of volatility (the process q is constant at all t ).…”