This project explores a bivariate copula-based approach to statistical arbitrage in financial markets. By modeling the joint dependence structure between two stock price series, copulas enable flexible and accurate representation of complex, non-linear relationships beyond linear correlation. The analysis employs both Elliptical copulas (Gaussian and Student's t) and Archimedean copulas (Clayton, Gumbel, Frank, Joe) to capture varying dependence patterns. The best-fitting copulas are selected using goodness-of-fit criteria and then used to construct a pair-trading strategy based on conditional probability thresholds, with subsequent backtesting to evaluate performance.