Implicit quantiles and expectiles

We compute nonparametric and forward-looking option-implied quantile and expectile curves, and we study their properties on a 5-year dataset of weekly options written on the S&P 500 Index. After studying the dynamics of the single curves and their joint behaviour, we investigate the potentiality of these quantities for risk management and forecasting purposes. As an alternative form of variability mesaures, we compute option-implied interquantile and interexpectile differences, that are compared with a weekly VIX-like index. In terms of forecasting power we investigate how different quantities related to the implicit quantile and expectile curves predict future logreturns and future realized variances.