# PENENTUAN HARGA KONTRAK OPSI TIPE ASIA MENGGUNAKAN MODEL SIMULASI NORMAL INVERSE GAUSSIAN (NIG)

• I PUTU OKA PARAMARTHA Faculty of Mathematics and Natural Sciences, Udayana University
• KOMANG DHARMAWAN Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University
• DESAK PUTU EKA NILAKUSMAWATI Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

### Abstract

The aim to determine of the simulation results and to calculate the stock price of Asian Option with Normal Inverse Gaussian (NIG) method and Monte Carlo method using MATLAB program. Results of both models are compared and selected a fair price. Besides to determine simulation accuracy of the stock price, speed of program execution MATLAB is calculated for both models for time efficiency. The first part, set variabels used to calculate the trajectory of stock prices at time t to simulate the stock price at the time. The second part, simulate the stock price with NIG model. The third part, simulate the stock price with Monte Carlo model. After simulating the stock price, calculated the value of the pay-off of the Asian Option, and then estimate the price of Asian Option by averaging the entire value of pay-off from each iteration. The last part, compare result of both models. The results of this research is price of Asian Option calculated using Monte Carlo simulation and NIG. The rates were calculated using the NIG produce a fair price, because of the pricing contract NIG using four parameters ?, ?, ?, and ?, while Monte Carlo is using only two parameters ? and ?. For execution time of the program, the Monte Carlo model is better in all iterations.

### Author Biographies

I PUTU OKA PARAMARTHA, Faculty of Mathematics and Natural Sciences, Udayana University
Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University
KOMANG DHARMAWAN, Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University
Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University
DESAK PUTU EKA NILAKUSMAWATI, Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University
Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University
Published
2014-08-29
How to Cite
PARAMARTHA, I PUTU OKA; DHARMAWAN, KOMANG; NILAKUSMAWATI, DESAK PUTU EKA. PENENTUAN HARGA KONTRAK OPSI TIPE ASIA MENGGUNAKAN MODEL SIMULASI NORMAL INVERSE GAUSSIAN (NIG). E-Jurnal Matematika, [S.l.], v. 3, n. 3, p. 123 - 129, aug. 2014. ISSN 2303-1751. Available at: <https://ojs.unud.ac.id/index.php/mtk/article/view/12003>. Date accessed: 02 june 2023. doi: https://doi.org/10.24843/MTK.2014.v03.i03.p074.
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### Keywords

Option; Asian Option; Normal Inverse Gaussian; NIG; Monte Carlo