Judul: Stock Price Simulation Using Geometric Brownian Motion (GBM) and Variance Gamma (VG) processes
Abstrak: Investasi merupakan penempatan sejumlah dana saat ini untuk memperoleh manfaat di masa yang akan datang. Investasi yang banyak menarik investor khususnya di bidang finansial adalah investasi di pasar modal. Salah satu surat berharga yang banyak diperdagangkan di pasar modal adalah saham. Keuntungan investasi saham dapat dilihat dari nilai return saham. Pergerakan harga saham yang mengikuti proses stokastik bergerak acak pada selang waktu tertentu yang menyebabkan harga saham sulit untuk diprediksi, sehingga digunakan metode Monte Carlo untuk memprediksi harga saham yang terjadi. Penelitian ini bertujuan melakukan simulasi Monte Carlo dalam menentukan harga saham menggunakan proses Geometric Brownian Motion (GBM) dan Variance Gamma (VG), serta membandingkan statistik deskriptifmya. Adapun sumber data yang yang digunakan adalah harga saham mingguan Microsoft periode 1 Januari 2015 − 31 Desember 2019. Berdasarkan hasil yang didapatkan, simulasi menggunakan proses GBM nilai statistik deskriptifnya lebih mengikuti pola data sebenarnya dengan nilai Mean Absolute Scaled Error yang lebih kecil dibandingkan dengan simulasi proses VG., Investment is the placement of a number of funds today to obtain benefits in the future. Investments that attract many investors, especially in the financial sector, are investments in the capital market. One of the securities that are widely traded in the capital market is shares. The advantages of stock investment can be seen from the value of stock returns. The movement of stock prices following a stochastic process moves randomly at certain intervals which makes stock prices difficult to predict, so the Monte Carlo method is used to predict stock prices that occur. This study aims to conduct a Monte Carlo simulation in determining stock prices using Geometric Brownian Motion (GBM) and Variance Gamma (VG) processes, as well as comparing descriptive statistics. The data source used is Microsoft's weekly stock price for the period 1 January 2015 – 31 December 2019. Based on the results obtained, the simulation using the GBM process has a descriptive statistical value that follows the actual data pattern with a smaller Mean Absolute Scaled Error value compared to the simulation of the VG process.
Keyword: Geometric Brownian Motion (GBM), Monte Carlo simulation, return, stock, Variance Gamma (VG)

Judul: Comparing the Accuracy of Geometric Brownian  Motion and ARIMA Models in Predicting the BIRD Stock Prices
Abstrak: Saham merupakan salah satu instrumen investasi yang dapat dipilih untuk memperoleh keuntungan di masa yang akan datang. Harga saham bergerak fluktuatif mengikuti proses stokastik. Model matematika diperlukan dalam membaca pergerakan saham, misalnya model Geometric Brownian Motion (GBM) dan Autoregressive Integrated Moving Average (ARIMA). Penelitian ini bertujuan untuk membandingkan tingkat keakuratan model GBM dan ARIMA dalam memprediksi harga saham. Data yang digunakan adalah harga penutupan saham PT Blue Bird Tbk periode 11 Februari 2023 – 11 Februari 2024. Data tersebut dibagi menjadi data training sebanyak 191 data dan data testing sebanyak 46 data. Di antara model ARIMA, model ARIMA(4,1,4) adalah model terbaik dengan nilai AIC sebesar 2008.16 dan semua parameternya signifikan pada taraf nyata 5%. MAPE dipilih menjadi alat dalam mengukur tingkat keakuratan model dalam kinerjanya memprediksi harga saham karena data yang digunakan tidak memiliki pencilan. Berdasarkan hasil penelitian diperoleh nilai MAPE model GBM sebesar 10.3634%, sedangkan model ARIMA(4,1,4) sebesar 7.7838%., Stocks are one of the investment instrumens that can be chosen to obtain profits in the future. Stock prices fluctuate following a stochastic process. Mathematical models, such as Geometric Brownian Motion (GBM) and Autoregressive Integrated Moving Average (ARIMA) models, can be used in reading stock movements. This study aims to compare the accuracy of GBM and ARIMA models in predicting stock prices. The data used are the closing price of PT Blue Bird’s Tbk shares for the period February 11, 2023 – Februari 11, 2024. The data are divided into 191 training data and 46 testing data. Among the ARIMA models, the ARIMA(4,1,4) was the best model with an AIC value of 2008.16 and all its parameters were significant at level 5%. MAPE was chosen as a tool in measuring accuracy of the model in predicting stock prices because the data used do not have outliers. Based on the results of the study, the MAPE value of GBM model was 10.36345%, while the MAPE value of ARIMA(4,1,4) model was 7.783817%.
Keyword: ARIMA, MAPE, Blue Bird, gbm, stock

Judul: Posisi Filogenetik Kura-Kura Carettochelys Insculpta  (Reptillia: Testudinata)
Abstrak: Carettochelys insculpta is an endemic freshwater turtle of southern Papua and northern Australia. Phylogenetic position of this turtle is remain unresolved until now. Most of the research conducted show close relationships of C. insculpta and members of Trionychidae family. However, some of the research show distance between C. insculpta and members of Trionychidae family. This research is conducted to analyze phylogenetic relationship between C. insculpta and other members of Testudinata using 12S rRNA, 16S rRNA, and both gene as markers. DNA samples were obtained from three different organisms of C. insculpta. Two species used as outgroups were Alligator mississippiensis and Iguana iguana. Phylogenetic analysis was carried out using Neighbor-Joining method with Felsenstein 1981 (F81) modeltest. A polytomy tree of Testudinata was produced by using 12S rRNA gene. However, analysis using 16S rRNA and both genes as markers confirmed that C. insculpta was located between the Chelonidae and the Trionychidae family.
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