This study aimed to predict the JKII (Jakarta Islamic Index) price as a price index of sharia stocks and predict the loss risk. This study uses geometric Brownian motion (GBM) and Value at Risk (VaR; with the Monte Carlo Simulation approach) on the daily closing price of JKII from 1 August 2020–13 August 2021 to predict the price and loss risk of JKII at 16 August 2021–23 August 2021. The findings of this study were very accurate for predicting the JKII price with a MAPE value of 2.03%. Then, using VaR with a Monte Carlo Simulation approach, the loss risk prediction for 16 August 2021 (one-day trading period after 13 August 2021) at the 90%, 95%, and 99% confidence levels was 2.40%, 3.07%, and 4.27%, respectively. Most Indonesian Muslims have financial assets in the form of Islamic investments as they offer higher returns within a relatively short time. The movement of all Islamic stock prices traded on the Indonesian stock market can be seen through the Islamic stock price index, namely the JKII (Jakarta Islamic Index). Therefore, the focus of this study was predicting the price and loss risk of JKII as an index of Islamic stock prices in Indonesia. This study extends the previous literature to determine the prediction of JKII price and the loss risk through GBM and VaR using a Monte Carlo simulation approach.

Farmer Exchange Rate (FER) is an indicator that can be used to measure the level of farmers welfare. For every agriculture sector, FER is affected by the historical price of harvest from the corresponding sector and historical prices of other agriculture sectors. In Central Java Province, rice & palawija, horticulture, and fisheries are the largest agriculture sectors which is the main livelihood for most of the population. FER forecasting is a crucial thing to determine the level of farmers welfare in the future. One method that can be used to predict the value of a variable that is influenced by the historical value of several variables is Vector Time Series. An empirical study was conducted using FER data from the rice & palawija, horticulture and fisheries sectors for January 2011-June 2017 in Central Java Province. The results obtained show that by using the VIMA(2.1) model, the FER prediction was very accurate, with MAPE values were 1.91% (rice & palawija sector), 2.44% (horticulture sector), and 2.18% (fisheries sector).

Saham merupakan salah satu emiten yang paling banyak diperjualbelikan di pasar modal. Harga saham dan perubahannya merupakan dua indikator yang sering dijadikan bahan pertimbangan oleh para calon investor sebelum memutuskan untuk membeli saham suatu perusahaan. Harga saham hampir selalu mengalami perubahan, dan sulit diperkirakan bagaimana keadaannya pada periode yang akan datang. Terdapat berbagai metode yang dapat digunakan untuk memperikirakan harga saham pada periode yang akan datang. Diantaranya adalah pemodelan dengan Geometric Brownian Motion (GBM) dan pemodelan dengan GeometricBrownian Motion (GBM) dengan Jump. Metode GBM dapat memperediksi harga saham dengan baik apabila data return saham periode sebelumnya berdistribusi normal. Sedangkan jika pada data return saham periode sebelumnya memenuhi asumsi normalitas dan ditemukan adanya lompatan, maka digunakan metode Jump Diffusion. Prediksi harga saham AALI untuk periode 03/01/2017 sampai dengan 12/05/2017 dengan GBM menghasilkan akurasi peramalan yang baik, dengan nilai MAPE sebesar 11,26%. Prediksi harga saham AALI untuk periode 03/01/2017 sampai dengan 12/05/2017 dengan metode Jump Diffuison menghasilkan akurasi peramalan yang sangat baik, dengan nilai MAPE sebesar 2,60%. Berdasarkan nilai MAPE, model Jump Diffusion memberikan hasil yang lebih baik daripada model GBM.

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Stocks portfolio is a form of investment that can be used to minimize the risk of loss. In a stock portfolio, the value at risk (VaR) can be predicted through the portfolio return. If portfolio return variance is heteroscedastic risk prediction can be done by using VaR with ARIMA-GARCH or Ensemble ARIMA-GARCH model approach. Furthermore, the accuracy of VaR is tested through backtesting test. In this study, the portfolio formed from Astra Agro Lestari Ltd (AALI) and Indofood Ltd (INDF) stocks from 10/02/2012 to 10/01/2019. The results showed that the best model is ARIMA(0,0,[3])-GARCH(1,2) with AIC of -5.604 and MSE 1.874e-07.At confidence level of 95% and 1 day holding period, the VaR of the ARIMA(0,0,[3])-GARCH(1,2) was -0.3464. Based on the backtesting test, it is proven to be very accurate to predict the value of loss risk because the value of the violation ratio (VR) is equal to 0.