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We develop Bayesian Markov chain Monte Carlo methods for inferences of continuous-time models with stochastic volatility and infinite-activity Lévy jumps using discretely sampled data. Simulation studies show that (i) our methods provide accurate joint identification of diffusion, stochastic volatility, and Lévy jumps, and (ii) affine jump-diffusion models fail to adequately approximate the behavior of infinite-activity jumps. In particular, the affine jump-diffusion models fail to capture thedoi:10.2139/ssrn.891135 fatcat:e72e3ixi5fcwrdrkpoms6q3lzy