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The average value at risk (AVaR) is a measuring tool used to assess the worst loss experienced by an investor on a portfolio investment at a certain time. Furthermore. AVaR's level of confidence needs to fulfill all the axioms regarding the nature of risk for risk-varse investors. This is because the possibility of an asymmetric volatility response can be overcomed by estimating the risk of loss using the Glosten. Jagganathan. and Runkle (GJR) models. In this study. the stock price data for the period January 1-28 December 2018 were used for the response. Therefore. this study aims to determine the risk estimation of stock price loss using the Average Value at Risk with the Glosten Jagganathan and Runkle models. The results showed that the stock price obtained from the AVaR estimation with a 95% confidence level of 0.1627% may be experienced one day ahead.

The European call option is a contract that gives the contract holder the right to buy a certain asset at a price and a certain period of time, which is the execution time at maturity. This study aims to determine the accuracy of the simulation results of stock prices to determine the price of European call options from simulation of standard Monte Carlo and the antithetic variates technique using R-Studio software. The results of the simulation of the two methods will approach the option price of the analytic solution. Analytical solutions in this study use the Black-Scholes model to obtain a standard price that serves to compare the two methods. The call option price of the European type uses the Black-Scholes model as a benchmark is $ 14.20281. In the 1.000.000 th standard Monte Carlo simulation, the call option price converges to $14.69786 with a standard error of 0.019, while the 100.000 th Monte Carlo-antithetic variates produces a call option price converges at $14.69801 with a standard error of 0.043. The results of this study indicate that Monte Carlo simulation with antithetic variates technique is more accurate because it produces an option value faster to converge with a relatively smaller standard error.

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