Optimizing Exotic Option Pricing: Monte Carlo Simulation and Variance Reduction Techniques

This study investigates the pricing of exotic options, specifically Barrier and Asian options, through the application of Monte Carlo simulation. The research commences by establishing the theoretical foundations and closed-form solutions within the Black-Scholes framework. Subsequently, three distinct random walk models are introduced to generate underlying asset paths for simulation purposes. The antithetic variate technique is demonstrated to significantly reduce standard error and accelerate convergence in the pricing of both options, thereby enhancing the precision of Monte Carlo estimates. Notably, the selection of underlying random walk models is found to have a minimal impact on accuracy, suggesting avenues for further research in advanced variance reduction techniques. This study provides valuable insights into the pricing of exotic options, offering implications for finance professionals and researchers, and driving innovation in option pricing methodologies for dynamic financial markets. The research underscores the efficacy of Monte Carlo simulation and variance reduction techniques in pricing complex options, contributing to the advancement of financial modelling and derivatives pricing.