The aims of this paper are twofold. First, to investigate the accuracy of different option-implied trees in pricing European options in order to assess the power of implied trees in replicating the market information. Second, to compare deterministic volatility implied trees and stochastic implied volatility models (Bakshi et al. (2003)) in assessing the forecasting power of implied moments on subsequently realised moments, and ascertaining the existence, magnitude and sign of variance, skewness, and kurtosis risk-premia. The analysis is carried out using the Italian daily market data covering the period 2005-2014. This enables us to contrast the pricing performance of implied trees and to assess the magnitude and sign of risk premia in both a tranquil and a turmoil period. The findings are as follows. First, the pricing performance of the Enhanced Derman and Kani (EDK, Moriggia et al. 2009) model is superior to that of the Rubinstein (1994) model. This superiority is stronger especially in the high volatility period due to a better estimation of the left tail of the distribution describing bad market conditions. Second, the Bakshi et al. (2003) formula is the most accurate for forecasting skewness and kurtosis, while for variance it yields upwardly biased forecasts. All models agree on the signs of the risk premia: negative for variance and kurtosis, and positive for skewness, but differ in magnitude. Overall, the results suggest that selling (buying) variance and kurtosis (skewness) is profitable in both high and low volatility periods.