PRICING OF CALL OPTIONS USING THE QUASI MONTE CARLO METHOD

  • Indah Oktaviani Statistics Study Program, Faculty of Mathematics and Natural Sciences, Tanjungpura University, Indonesia
  • Evy Sulistianingsih Statistics Study Program, Faculty of Mathematics and Natural Sciences, Tanjungpura University, Indonesia
  • Neva Satyahadewi Statistics Study Program, Faculty of Mathematics and Natural Sciences, Tanjungpura University, Indonesia
DOI: https://doi.org/10.30598/barekengvol17iss4pp1949-1956
Keywords: Call Options, Halton's Quasi-Random, Quasi Monte Carlo

Abstract

A call option is a type of option that grants the option holder the right to buy an asset at a specified price within a specified period of time. Determining the option price period of time within a certain period of time is the most important part of determining an investment strategy. Various methods can be employed to determine the prices of options, such as Quasi-Monte Carlo and Monte Carlo simulations. The purpose of this research is to determine the price of European-type call options using the Quasi-Monte Carlo method. The data used is daily stock closing price data on the Apple Inc. for the period October 1, 2021, to September 30, 2022. Apple Inc. stock options in this study were chosen because it is the largest technology company in the world in 2022. The steps taken in this study are to determine the parameters obtained from historical data such as the initial risk-free interest rate (r), stock price (, volatility , maturity time (T), and strike price (K). Next is to generate Halton’s quasi-randomized sequence and simulate the stock price by substituting the parameters  by substituting the parameters. Then proceed to calculate the call option payoff and estimate the call option price by averaging the call option payoff values. The results showed that the call option price of the company Apple Inc. using the Quasi-Monte Carlo with Halton’s quasi-randomized sequence on the 1000000th simulation with a standard error of 0,045 is $90,163. The call option price obtained can be used as a reference for investors in purchasing options to minimize losses from call option investments in that period.

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References

I. M. Adnyana, Manajemen Investasi dan Portofolio, Jakarta Selatan: Lembaga Penerbitan Universitas Nasional (LPU-UNAS), 2020.

W. W. Hidayat, Konsep Dasar Investasi dan Pasar Modal, Jawa Timur: Uwais Inspirasi Indonesia, 2019.

D. P. I. Putri, W. Alwi, and I. Syata, “Penentuan Harga Kontrak Opsi Tipe Amerika Menggunakan Quasi Monte Carlo,” Jurnal MSA (Matematika dan Statistika serta Aplikasinya), vol. 6, no. 2, pp. 45-50, 2018.

D. A. A. P. Ratnasari, K. Dharmawan, and D. P. E. Nilakusmawati, “Penentuan Nilai Kontrak Opsi Tipe Binary Pada Komoditas Kakao Menggunakan Metode Quasi Monte Carlo Dengan Barisan Acak Faure,” E-Jurnal Matematika, vol. 6, no. 4, pp. 214-219, November 2017.

I. G. P. N. Mahayoga, K. Dharmawan, L. P. I. Harini, “Penentuan Harga Kontrak Opsi Tipe Eropa Menggunakan Metode Quasi Monte Carlo Dengan Barisan Kuasi-Acak Halton,” E-Jurnal Matematika, vol. 3, no. 4, pp. 154-159, November 2014.

S. A. Putri, B. Subartini, and Sukono, “The Use of Quasi Monte Carlo Method with Halton Random Number Sequence in Determining the Price of European Type Options (Case in PT Telekomunikasi Indonesia Stock’s),” International Journal of Global Operations Research, vol. 3, no. 4, pp. 116-124, 2022.

R. Syam, A. Zaki, and M. H. Basri, “Prediksi Harga Kontrak Opsi Asia Dalam Perdagangan Pasar Saham Dengan Menggunakan Metode Monte Carlo,” Journal of Mathematics, Computations, and Statistics, vol. 1, no. 1, pp. 31-37, April 2018.

L. W. Aeli, D. Devianto, and H. Yozza, “Penggunaan Metode Simulasi Quasi Monte Carlo Dengan Barisan Quasi Acak Van Der Courput Dalam Menentukan Harga Opsi Eropa,” Jurnal Kajian Matematika dan Aplikasinya, vol. 3, no. 2, pp. 33-40, 2022.

A. B. Owen, “A Randomized Halton Algorithm In R,” paper Arxiv, Stanford University, 2017.

N. N. A. Artanadi, K. Dharmawan, and K. Jayanegara, “Penentuan Harga Opsi Beli Tipe Asia Dengan Metode Monte Carlo-Control Variate,” E-Jurnal Matematika, vol. 6, no. 1, pp. 29-36, Januari 2017.

T. N. Habaib, S. Mariani, and R. Arifudin, “Penentuan Harga Opsi Asia Menggunakan Metode Simulasi Monte Carlo dengan Teknik Reduksi Variansi,” UNNES Journal of Mathematics, vol. 7, no. 1, pp. 28-37, 2018.

Lusiana, S. Martha, and S. W. Rizki, “Penentuan Harga Saham Menggunakan Pendekatan Metode Monte Carlo,” Buletin Ilmiah Matematika, Statistika, Dan Terapannya (Bimaster), vol. 7, no. 2, pp. 119-126, 2018.

T. Trimono, D.A. I. Maruddani and D. Ispriyanti, “Pemodelan Harga Saham Dengan Geometric Brownian Motion dan Value At Risk PT Ciputra Development Tbk,” Jurnal Gaussian, vol. 6, no. 2, pp. 261-270, 2017.

G. Supriadi, Statistik Penelitian Pendidikan, 1st ed., Yogyakarta: UNY Press, 2021.

N. Pratiwi, E. Sulistianingsih, and N. Imro’ah, “Penggunaan Metode Greeks Black Scholes Untuk Analisis Sensitivitas Harga Opsi Beli Eropa,” Bimaster: Buletin Ilmiah Terapan Matematika, Statistika, dan Terapannya, vol. 8, no. 2, pp. 363-370, 2019.

J. Demgne, W. Lair, J. Lonchampt, and S. Mercier, “An Application Of Quasi Monte Carlo Methods For The Numerical Assessment Of Maintenance Strategies,” 25th European Safety and Reliability Conference, pp. 907-916, 2015.

T. O. Mukhti, D. Devianto, and H. Yozza, “Simulasi Quasi Monte Carlo menggunakan Barisan Quasi Acak Halton,” Jurnal Matematika UNAND, vol. 7, no. 2, pp. 221-228, 2018.

J. A. P. Sumampouw, C. E. J. C. Montolalu, and T. Manurung, “Metode Quasi Monte Carlo Dengan Barisan Bilangan Acak Halton Dalam Menentukan Nilai Kontrak Opsi Tipe Binary Pada Saham PT. Gudang Garam, Tbk,” d’Cartesian; Jurnal Matematika dan Aplikasi, vol. 9. no. 2. pp. 140-144, 2021.

Published
2023-12-18
How to Cite
[1]
I. Oktaviani, E. Sulistianingsih, and N. Satyahadewi, “PRICING OF CALL OPTIONS USING THE QUASI MONTE CARLO METHOD”, BAREKENG: J. Math. & App., vol. 17, no. 4, pp. 1949-1956, Dec. 2023.
Issue
Vol 17 No 4 (2023): BAREKENG: Journal of Mathematics and Its Applications
Section
Articles

Copyright (c) 2023 Indah Oktaviani, Evy Sulistianingsih, Neva Satyahadewi

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