PENENTUAN NILAI VALUE at RISK PADA SAHAM IHSG MENGGUNAKAN MODEL GEOMETRIC BROWNIAN MOTION DENGAN LOMPATAN

  • I GEDE ARYA DUTA PRATAMA Faculty of Mathematics and Natural Sciences, Udayana University
  • KOMANG DHARMAWAN Faculty of Mathematics and Natural Sciences, Udayana University
  • LUH PUTU IDA HARINI Faculty of Mathematics and Natural Sciences, Udayana University

Abstract

The aim of this research was to measure the risk of the IHSG stock data using the Value at Risk (VaR). IHSG stock index data typically indicates a jump. However, Geometric Brownian Motion (GBM) model can not catch any of the jumps. To view the jumps, it is necessary that the model was then developed into a Geometric Brownian Motion (GBM) model with Jumps. On the GBM model with Jumps, returns the data are discontinuous. To determine the value of VaR, the value of return to perform the simulation model of GBM with Jumps is required. To represent processes that contain jumps, discontinuous Poisson process using the Peak-Over Threshold is required. To determine the parameters of model, calibration of historical data using the Maximum Likelihood Estimation (MLE) method is performed. VaR value for GBM model with Jumps with a 95% and 99% confidence level are -0,0580 and -0,0818 while VaR value for GBM model with a 95% and 99% confidence level are -0,0101 and -0,0199. VaR for GBM model with Jumps with a confidence level of 95% and 99% show greater than the model VaR for GBM.

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Author Biographies

I GEDE ARYA DUTA PRATAMA, Faculty of Mathematics and Natural Sciences, Udayana University
Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University
KOMANG DHARMAWAN, Faculty of Mathematics and Natural Sciences, Udayana University
Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University
LUH PUTU IDA HARINI, Faculty of Mathematics and Natural Sciences, Udayana University
Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University
Published
2015-05-30
How to Cite
PRATAMA, I GEDE ARYA DUTA; DHARMAWAN, KOMANG; IDA HARINI, LUH PUTU. PENENTUAN NILAI VALUE at RISK PADA SAHAM IHSG MENGGUNAKAN MODEL GEOMETRIC BROWNIAN MOTION DENGAN LOMPATAN. E-Jurnal Matematika, [S.l.], v. 4, n. 2, p. 67 - 73, may 2015. ISSN 2303-1751. Available at: <https://ojs.unud.ac.id/index.php/mtk/article/view/13550>. Date accessed: 08 aug. 2022. doi: https://doi.org/10.24843/MTK.2015.v04.i02.p091.
Section
Articles

Keywords

Geometric Brownian Motion with Jumps; Return; Value at Risk

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