We price S&P 500 index options under the assumption that the conditional risk-neutral density function of the index follows a Semi-Nonparametric (SNP) process with GARCH variance. The model is estimated combining a set of option contracts written on the index and the daily index return time series in the period 1996-2011. The in-sample and out-sample performance of the model is compared with several benchmark models, beating most of them. We conclude that a pricing model dealing simultaneously with non-normalities and time-varying volatility helps to mitigate the observed S&P 500 index option biases. (c) 2015 Wiley Periodicals, Inc. Jrl Fut Mark 36:217-239, 2016