Perbandingan Metode Monte Carlo Standar, Control Variate, dan Antithetic Variate pada Estimasi Harga dan Interval Kepercayaan Opsi Asia Rataan Aritmatika

Abstract

The pricing of arithmetic average Asian options is commonly performed using Monte Carlo simulation because no closed-form analytical solution is available. However, the standard Monte Carlo method suffers from high estimator variance, requiring a large number of simulations to achieve accurate estimates. This study compares the performance of the Standard Monte Carlo, Control Variate, and Antithetic Variate methods in estimating option prices and confidence intervals for arithmetic average Asian call and put options. Numerical simulations were conducted under the Geometric Brownian Motion model using identical parameters for all methods so that differences in the results were solely attributable to the estimation techniques. The number of simulations was varied to investigate convergence behavior and the corresponding 95% confidence intervals. The results indicate that all methods converge as the number of simulations increases, while the confidence intervals become progressively narrower. The Antithetic Variate method provides more stable estimates than the Standard Monte Carlo method by reducing estimator variance through negatively correlated random pairs. Among the three methods, the Control Variate method consistently produces the most stable estimates and the narrowest confidence intervals for both call and put options. These findings demonstrate that the Control Variate method is the most efficient and accurate approach for pricing arithmetic average Asian options.