This thesis studies several practical issues in asset pricing, including MCMC estimation of time-changed Lévy processes, calibration techniques for stochastic volatility models, and a sampling scheme for the SABR model. First, a MCMC estimation approach is developed to estimate time-changed Lévy processes. Simulation-based experiments demonstrate good accuracy of the MCMC approach. An empirical study on its fitness of the return dynamics is provided, which shows that time-changed Lévy models can achieve excellent performance in capturing index returns. Second, a further study on MCMC estimation is applied to multivariate Lévy processes, in order to evaluate the efficiency and accuracy of the Bayesian technique for high-dimensional portfolio theory. Last, a new representation of the SABR model is proposed by adopting a coupling approach, based on which, the uncorrelated SABR is sampled from its density. Numerical experiments are implemented to compare the sampling scheme with the Euler discretization scheme and examine the accuracy of Hagan’s popular formula for the implied Black-Scholes volatility.