This study is one of the first to utilize the stochastic volatility (SV) model to modelling the Peruvian financial times series. We estimate and compare this model with generalized autoregressive conditional heteroscedasticity (GARCH) models with normal and t-student errors. The analysis in this study corresponds to Peru’s stock market and exchange rate returns. The importance of this methodology is that the adjustment of the data is better than the GARCH models, using the assumptions of normality in both models. In the case of the SV model, three Bayesian algorithms have been employed where we evaluate their respective inefficiencies in the estimation of the model’s parameters—the most efficient being the integration sampler. The estimated parameters in the SV model under the various algorithms are consistent, as they display little inefficiency. The figures of the correlations of the iterations suggest that there are no problems at the time of Markov chaining in all estimations. We find that the volatilities in the exchange rate and stock market volatilities follow similar patterns over time. That is, when economic turbulence caused by the economic circumstances occurred, for example, the Asian crisis and the recent crisis in the USA, considerable volatility was generated in both markets. JEL Classification: C22.