# MENENTUKAN HARGA KONTRAK BERJANGKA NILAI TUKAR RUPIAH TERHADAP DOLLAR AS MENGGUNAKAN DISTRIBUSI LOGNORMAL

• GEDE SUMENDRA Faculty of Mathematics and Natural Sciences, Udayana University
• KOMANG DHARMAWAN Faculty of Mathematics and Natural Sciences, Udayana University
• I NYOMAN WIDANA Faculty of Mathematics and Natural Sciences, Udayana University

### Abstract

The purpose of this study is to determine the fair price of a futures contract for the IDR (Rupiah) against the USD using lognormal distribution simulation. This result is compared with interest rate parity theorem. The first step of this study is to determine the values of the parameters which are optimized using Maximum Likelihood Estimation (MLE). The parameters obtained in the form of the mean () and variance (). Further, parameters obtained are simulated using lognormal distribution to determine the exchange rate simulation (). Then price of future contract is also calculated using interest rate parity theorem. The price of the futures contracts () is determined by lognormal distribution simulated and price of interest rate futures contracts using parity theorem. The results of this study show that future contract price over the fair use lognormal distribution of 12.215 compared to the interest rate parity theorem which 12.400, with the initial contract price () of 12.185.

### Author Biographies

GEDE SUMENDRA, 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
I NYOMAN WIDANA, 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
SUMENDRA, GEDE; DHARMAWAN, KOMANG; WIDANA, I NYOMAN. MENENTUKAN HARGA KONTRAK BERJANGKA NILAI TUKAR RUPIAH TERHADAP DOLLAR AS MENGGUNAKAN DISTRIBUSI LOGNORMAL. E-Jurnal Matematika, [S.l.], v. 4, n. 2, p. 43 - 48, may 2015. ISSN 2303-1751. Available at: <https://ojs.unud.ac.id/index.php/mtk/article/view/13469>. Date accessed: 03 july 2022. doi: https://doi.org/10.24843/MTK.2015.v04.i02.p087.
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### Keywords

derivatives; futures contracts; the exchange rate against the USD; lognormal distribution; interest rate parity theorem