Aplikasi Simulasi Monte Carlo Dengan Teknik Antithetic Variates Dalam Menentukan Harga Opsi Cash-or-nothing Call

Abstract

Monte Carlo method is the basis of all algorithms of the simulation method based on solving a problem to get better results by giving as many numbers of random numbers that generated and spread to normal standards. Antithetic variates method is one of the variance reduction methods to improve efficiency in Monte Carlo simulations. The problem of this research is how much the price of price of the European cash-or-nothing call option using Monte Carlo simulation with antithetic variates technique, and to check the accuracy of the results of the method calculated relative error, the smaller the relative error is, the more accurate the results obtained from the numerical method. By using the stock price data from the computed NASDAQ Composite with initial stock price (S0) of $ 8475.31, strike price (K) of $ 8470, maturity (T) which is 1 year, interest free rate (r) is 2.25%, and volatility (σ) is 0.1935467, a number of simulations (N) of 10.000.000, thus the price of NASDAQ European cash-or-nothing call option NASDAQ Composite stock uses Monte Carlo method with an antithetic variates technique of $ 0.497710 with an error of 0.000051. From several simulation experiments starting from 1.000, 10.000, 100.000, 1.000,000, and 10.000.000, it shows that the more simulations carried out, the more converging the results obtained to the analytical solution, the Black-Scholes Model is $ 0.497735