In this study, Pairs Trading (PT) is considered. An example of its application using real data is shown and a time series simulation of the Saudi stock market using the Vector Auto-Regressive model (VAR) is performed on two stocks. In addition, the influence of different simulation model parameters on the total profit is investigated. We conducted a quantitative analysis of different cross-correlations that occurred between simulated stocks, as well as of different values of linear trends in the auto-regressive model. Furthermore, the optimal conditions for the application of a PT strategy, as well as the optimal parameters used for this strategy were obtained. It was shown that parallel trends and a high correlation between considered stocks can lead to significant profits. In the case of highly correlated series with limited volatility, benchmarks should be used for opening and closing positions.