This paper explores the application of Monte Carlo (MC), Quasi-Monte Carlo (QMC), and Randomized Quasi-Monte Carlo (RQMC) methods in the context of option pricing and risk analysis under the time-homogeneous hyperbolic local volatility (HLV) model. While standard MC methods suffer from slow convergence, QMC techniques leverage low-discrepancy sequences to achieve superior convergence rates, particularly for problems with low effective dimension. However, the deterministic nature of QMC prevents reliable error estimation, a limitation overcome by RQMC through randomized sequences such as Owen’s nested scrambling. The study incorporates variance reduction techniques such as Brownian Bridge (BB) and Principal Component Analysis (PCA) to reduce effective dimension and enhance convergence. Numerical experiments on Asian options demonstrate significant accuracy gains using RQMC over MC and QMC, especially when PCA is used. The paper also analyzes the convergence behavior and effective dimensions of price and Greeks (Delta, Gamma), confirming that RQMC-PCA offers the best performance in high dimensional settings. Joint work with Sergei Kucherenko.