Option Pricing Based on Several Monte Carlo Techniques

The Monte Carlo method is broadly used in financial technology and engineering for pricing complex derivatives and managing risk due to its flexibility and adaptability. However, Monte Carlo simulation may suffer from high variance problems, impacting accuracy and effectiveness. Control and antithetic variates are two main variance-reduction techniques to optimize the simulation. This paper compares the performance of normal Monte Carlo, and Monte Carlo optimized with control variates or antithetic variates in four different European options. In the work, the Monte Carlo optimization based on antithetic variates generally performs well, but in power options, the control variable method has a better effect on Monte Carlo optimization. By leveraging these variance reduction techniques, the accuracy and effectiveness of Monte Carlo simulations can be significantly enhanced, leading to more reliable option pricing. The results not only demonstrate the important role of variance-reduction techniques in the Monte Carlo method but also offer practical methods to improve option pricing strategy.