Aplikasi Simulasi Monte Carlo Dengan Teknik Antithetic Variates Dalam Menentukan Harga Opsi Cash-or-nothing Call

  • Ilham Syata Universitas Islam Negeri Alauddin Makassar


Monte Carlo method is the basis of all algorithms of the simulation method based on solving a problem to get better results by giving as many numbers of random numbers that generated and spread to normal standards. Antithetic variates method is one of the variance reduction methods to improve efficiency in Monte Carlo simulations. The problem of this research is how much the price of price of the European cash-or-nothing call option using Monte Carlo simulation with antithetic variates technique, and to check the accuracy of the results of the method calculated relative error, the smaller the relative error is, the more accurate the results obtained from the numerical method. By using the stock price data from the computed NASDAQ Composite with initial stock price (S0) of $ 8475.31, strike price (K) of $ 8470, maturity (T) which is 1 year, interest free rate (r) is 2.25%, and volatility (σ) is 0.1935467, a number of simulations (N) of 10.000.000, thus the price of NASDAQ European cash-or-nothing call option NASDAQ Composite stock uses Monte Carlo method with an antithetic variates technique of $ 0.497710 with an error of 0.000051. From several simulation experiments starting from 1.000, 10.000, 100.000, 1.000,000, and 10.000.000, it shows that the more simulations carried out, the more converging the results obtained to the analytical solution, the Black-Scholes Model is $ 0.497735

Author Biography

Ilham Syata, Universitas Islam Negeri Alauddin Makassar
Jurusan Matematika UIN Alauddin Makassar


M. N. Mooy, A. Rusgiono, and R. Rahmawati, “Penentuan harga opsi put dan call tipe eropa terhadap saham menggunakan model black-scholes,” GAUSSIAN, vol. 6, no. 3, pp. 407–417, 2017

D. P. Anggraini, D. C. Lesmana, and B. Setiawaty, “Aplikasi Simulasi Monte Carlo Untuk Menentukan Nilai Opsi Asia Dengan Menggunakan Metode Control Variate Pada Komoditas Pertanian,” J. Math. Its Appl., vol. 16, no. 1, pp. 69–82, 2017.

W. O. Irawan, M. Rosha, and D. Permana, “Penentuan Harga Opsi Dengan Model Black-Scholes Menggunakan Metode Beda Hingga Center Time Center Space (CTCS),” Eksakta, vol. 18, no. 2, 2017.

S. E. Fadugba and C. R. Nwozo, “Mellin Transform Method for the Valuation of the American Power Put Option with Non-Dividend and Dividend Yields,” J. Math. Financ., vol. 05, no. 03, pp. 249–272, 2015.

I. Kamila, E. H. Nugrahani, and D. C. Lesmana, “Metode Monte Carlo Untuk Menentukan Harga Opsi Barrier Dengan Suku Bunga Takkonstan,” J. Math. Its Appl., vol. 16, no. 1, pp. 55–68, 2017.

S. Wang, “A novel fitted finite volume method for the Black-Scholes equation governing option pricing,” IMA J. Numer. Anal., vol. 24, no. 4, pp. 699–720, 2004.

M. Gao, “The British Binary Option,” J. Math. Financ., vol. 9, pp. 747–762, 2019.

A. Paliathanasis, K. Krishnakumar, K. M. Tamizhmani, and P. G. L. Leach, “Lie symmetry analysis of the Black-Scholes-Merton Model for European options with stochastic volatility,” Mathematics, vol. 4, no. 2, pp. 1–14, 2016.

F. Black and M. Scholes, “The pricing of options and corporate l,” J. Polit. Econ., vol. 81, no. 3, pp. 637–654, 2008.

P. Jäckel, Monte Carlo methods in finance, Wiley Finance. 2002.

P. Glasserman, “Monte Carlo method in financial engineering,” Quantitative Finance, vol. 4, no. 4. pp. 46–47, 2004.

S. Ohsaki, J. Ruppert-Felsot, and D. Yoshikawa, R Programming and Its Applications in Financial Mathematics. 2017.

W. Ayudiah, D. C. Lesmana, and E. H. Nugrahani, “Penentuan Harga Opsi Sebagai Alat Lindung Nilai Petani Gabah Menggunakan Metode Monte Carlo Dan Teknik Control Variate,” J. Math. Its Appl., vol. 16, no. 1, p. 39, 2017.

How to Cite
Syata, I. (2020). Aplikasi Simulasi Monte Carlo Dengan Teknik Antithetic Variates Dalam Menentukan Harga Opsi Cash-or-nothing Call. Jurnal Matematika Dan Statistika Serta Aplikasinya , 8(1), 51 - 55. https://doi.org/10.24252/msa.v8i1.12866
Abstract viewed = 476 times