Variance Reduction Techniques for Monte Carlo Pricing of European Call Options

Monte Carlo simulation is one of many methods for pricing financial derivatives, such as European call options, but its slow convergence rate makes it nearly impossible to use in practice. This paper compares four Monte Carlo estimators for pricing a European call option under the Black-Scholes model: basic Monte Carlo, antithetic variates, control variates, and Quasi-Monte Carlo using Sobol low-discrepancy sequences. Using repeated simulations across multiple sample sizes, we measure the standard deviation of pricing errors relative to the analytical Black-Scholes value. Antithetic variates provide acceptable improvement, control variates yield substantially lower variance, and Quasi-Monte Carlo delivers the most impressive results, with variance reductions of up to two orders of magnitude. These results demonstrate the effectiveness of advanced sampling techniques in improving Monte Carlo efficiency.