Forecasting the mean and volatility of stock returns from option prices

In this paper we suggest a unified framework to predict the mean and volatility of stock log-returns from option prices adjusted for risk premium effects, which is free from any option pricing model. Based on this, the paper shows that both the physical mean and volatility do not correspond one-to-one to their risk neutral cumulants but depend on higher order cumulants, such as the third and the fourth ones capturing the degree of skewness and kurtosis of the risk neutral density, respectively. The results of the empirical analysis of the paper obtained based on our theoretical framework indicate that the risk premium effects can consistently explain the downward slope of the implied volatility or mean regressions to forecast future levels of their physical counterparts found in many studies. The estimates of the risk aversion coefficients are found not to be different than unity. Finally, based on a new regression model the paper shows that adjusting for risk premium effects can improve the ability of risk neutral cumulants to forecast the future movements in the physical mean and volatility from option prices. ∗Department of Accounting and Finance, Athens University of Economics and Business, email : [email protected]. †Department of Economics, Athens University of Economics and Business, email : [email protected].