Investment can be defined as an activity to postpone consumption at the present time with the aim to obtain maximum profits in the future. However, the greater the benefits, the greater the risk. For that we need a way to predict how much the risk will be borne. Modelling data that experiences heteroscedasticity and asymmetricity can use the Asymmetric Power Autoregressive Conditional Heteroscedasticity (APARCH) model. This research discusses the time series data risk analysis using the Value at Risk-Asymmetric Power Autoregressive Conditional Heteroscedasticity (VaR-APARCH) model using the daily closing price data of Bitcoin USD period January 1 2019 to 31 December 2019. The best APARCH model was chosen based on the value of Akaike's Information Criterion (AIC). From the analysis results obtained the best model, namely ARIMA (6,1,1) and APARCH (1,1) with the risk of loss in the initial investment of IDR 100,000,000 in the next day IDR 26,617,000. The results of this study can be used as additional information and apply knowledge about the risk of investing in Bitcoin with the VaR-APARCH model.

ini merupakan aplikasi metode Vector Autoregressive Exogenous (VARX) yang merupakan salah satu metode runtun waktu multivariat yang diaplikasikan untuk mencari besaran hubungan antara variabel endogen dengan variabel eksogen. Penelitian ini dilakukan untuk mengetahui ramalan suku bunga PUAB menggunakan metode VARX serta untuk melihat hubungan antara variabel suku bunga PUAB, BI rate, dan SIBOR. Ada beberapa tahapan dalam penelitian ini mulai dari menguji kestasioneran data hingga menguji hubungan antar variabel, atau dalam hal ini uji Kausalitas Granger. Penggunaan metode VARX dengan variabel endogen suku bunga PUAB dan BI rate serta variabel eksogen yaitu SIBOR menghasilkan model terbaik berdasarkan nilai AIC terkecil yaitu model VARX(2,1).

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.