Value at Risk (VaR) is a method to measure the maximum loss with a certain level of confidence in a certain period. Monte Carlo simulation is the most popular method of calculating VaR. The purpose of this study is to demonstrate control variates method as a variance reduction method that can be applied to estimate VaR. Moreover, it is to compare the results with the normal VaR method or analytical VaR calculation. Control variates method was used to find new returns from all stocks which are used as estimators of the control variates. The new returns were then used to define parameters needed to generate N random numbers. Furthermore, the generated numbers were used to find the VaR value. The method was then applied to estimate a portfolio of the game and esports company stocks that are EA, TTWO, AESE, TCEHY, and ATVI . The results show Monte Carlo simulation gives VaR of US$41.6428 within 1000 simulation, while the analytical VaR calculation or normal VaR method gives US$30.0949.
Stratification as a General Variance Reduction Method for Markov Chain Monte Carlo
