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

Abstract

We propose an implied volatility index for Brazil (called "IVol-BR"), based on daily market prices of options over IBOVESPA - an option market with relatively low liquidity and low number of option strikes. Our methodology combines usual international methodology used in high-liquidity markets with adjustments that take into account the low liquidity in Brazilian option market. We do a number of empirical tests to validate the IVol-BR. First, we show that the IVol-BR has significant predictive power over future volatility of equity returns not contained in traditional volatility forecasting variables. Second, we decompose the squared IVol-BR into (i) the expected variance of stock returns and (ii) the equity variance premium. This decomposition is of interest since the equity variance premium directly relates to the representative investor risk-aversion. Finally, we show empirically that higher risk-aversion is accompanied with higher expected returns, confirming the theory that high risk-aversion should be compensated by higher returns.