Stochastic volatility models (SVM) are commonly used to model time series data. They have many applications in finance and are useful tools to describe the evolution of asset returns. The motivation for this project is to determine if stochastic volatility models can be used to model Bitcoin exchange rates in a way that can contribute to an effective trading strategy. We consider a basic SVM and several extensions that include fat tails, leverage, and covariate effects. The Bayesian approach with the Particle Markov chain Monte Carlo (MCMC) method is employed to estimate the model parameters. We assess the goodness of the estimated model using the deviance information criterion. Simulation studies are conducted to assess the performance of Particle MCMC and to compare with the traditional MCMC approach. We then apply the proposed method to the Bitcoin exchange rate data and compare the effectiveness of each type of SVM.