This paper compares the option hedging and pricing performance of affine and non-affine stochastic volatility (SV) models with and without jumps in returns on a set of S\&P 500 option data from 2005 to 2009. The squared volatility index VIX serves as a proxy for the latent spot variance process, model parameter estimates of Christoffersen, Jacobs and Mimouni (2010) are used and all experiments are out-of-sample tests. The evaluation of hedging performance is based on the distribution of hedging errors and their dependency on the underlying for daily and weekly hedge rebalancing and different hedging strategies: delta, minimum-variance and delta-vega hedging. Pricing performance is mainly assessed based on implied volatility root mean squared errors, and both pricing and hedging error measures are decomposed along various dimensions. Monte Carlo methods are used to compute option sensitivities and prices and the theoretical backgrounds of the option pricing models and applied methodologies are outlined in detail. Different conclusions hold for the hedging (dynamic) and pricing (static) performance of the SV models investigated. For hedging, all SV models perform relatively similar, underperforming a simple ad-hoc Black-Scholes hedge for delta hedging, but with better results for minimum-variance and delta-vega hedging. No non-affine model is consistently better than the affine Heston (1993) model for hedging. Pricing errors suggest that a non-affine GARCH-type model with linear variance diffusion and drift specification performs best along virtually all dimensions, and that the VIX is a good proxy for its filtered spot variance path. Jumps have minor effects on pricing performance and virtually no effect on hedging performance for all models. Considering both hedging and pricing performance, advantages of the best performing non-affine model need to be considered in conjunction with its lack of analytical tractability that impose.