Summary In this paper we propose an efficient Markov chain Monte Carlo (MCMC) algorithm to estimate stochastic volatility models with jumps and affine structure. Our idea relies on the use of adaptive methods that aim at reducing the asymptotic variance of the estimates. We focus on the Delayed Rejection algorithm in order to find accurate proposals and to efficiently simulate the volatility path. Furthermore, Bayesian model selection is addressed through the use of reduced runs of the MCMC together with an auxiliary particle filter necessary to evaluate the likelihood function. An empirical application based on the study of the Dow Jones Composite 65 and of the FTSE 100 financial indexes is presented to study some empirical properties of the algorithm implemented.