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

Authors

  • Ilham Syata Universitas Islam Negeri Alauddin Makassar

DOI:

https://doi.org/10.24252/msa.v8i1.12866

Abstract

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

References

[1] 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
[2] 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.
[3] 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.
[4] 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.
[5] 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.
[6] 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.
[7] M. Gao, “The British Binary Option,” J. Math. Financ., vol. 9, pp. 747–762, 2019.
[8] 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.
[9] F. Black and M. Scholes, “The pricing of options and corporate l,” J. Polit. Econ., vol. 81, no. 3, pp. 637–654, 2008.
[10] P. Jäckel, Monte Carlo methods in finance, Wiley Finance. 2002.
[11] P. Glasserman, “Monte Carlo method in financial engineering,” Quantitative Finance, vol. 4, no. 4. pp. 46–47, 2004.
[12] S. Ohsaki, J. Ruppert-Felsot, and D. Yoshikawa, R Programming and Its Applications in Financial Mathematics. 2017.
[13] 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.

Downloads

Published

2020-07-06

How to Cite

[1]
I. Syata, “Aplikasi Simulasi Monte Carlo Dengan Teknik Antithetic Variates Dalam Menentukan Harga Opsi Cash-or-nothing Call”, MSA, vol. 8, no. 1, pp. 51–55, Jul. 2020.

Issue

Vol. 8 No. 1 (2020): Volume 8 Nomor 1

Section

Artikel

License

Copyright Notice

Jurnal MSA (Matematika dan Statistika serta Aplikasinya)

Authors who publish in Jurnal MSA agree to the following copyright and licensing terms.

1. Copyright Ownership

Authors retain copyright in their scholarly articles unless copyright is lawfully held by another authorized rights holder.

Publication in Jurnal MSA does not require an exclusive transfer or assignment of copyright ownership to the journal or its publisher.

2. Non-Exclusive Publishing Rights

Authors or authorized copyright holders grant Jurnal MSA non-exclusive rights of first journal publication, dissemination, indexing, and digital preservation.

These rights allow the journal to publish, reproduce, distribute, archive, and preserve the accepted scholarly article without transferring copyright ownership.

3. Publication License

Jurnal MSA adopts and applies the Creative Commons Attribution 4.0 International License (CC BY 4.0) as the standard license for scholarly articles published under its current publication terms.

Authors or authorized rights holders authorize publication of their articles under CC BY 4.0.

This license permits sharing, reproduction, redistribution, adaptation, and reuse, including commercial reuse, subject to the license terms and attribution requirements.

Official License:

https://creativecommons.org/licenses/by/4.0/

4. Non-Commercial Publishing Model

Jurnal MSA operates as a non-commercial scholarly publisher dedicated to education, scientific research, and scholarly communication.

The journal's non-commercial status does not restrict commercial reuse of articles licensed under CC BY 4.0.

5. Authors' Rights and Self-Archiving

Authors retain their applicable rights to reuse, share, and disseminate their scholarly works.

Authors may immediately deposit and distribute the published version of their CC BY 4.0-licensed articles through institutional repositories, disciplinary repositories, and academic websites without an embargo imposed by the journal.

Such distribution remains subject to the applicable license and third-party rights.

6. Author Consent and Third-Party Rights

By agreeing to publication, the corresponding author confirms that:

  1. All listed authors have approved the manuscript and the publication arrangements.

  2. The authors or authorized rights holders possess the legal authority necessary to authorize publication and licensing.

  3. Jurnal MSA is granted the necessary non-exclusive publishing rights.

  4. Publication of the article under CC BY 4.0 is authorized.

  5. Required permissions for third-party materials have been obtained, and any licensing exclusions have been clearly identified.

7. Previously Published Articles

Articles published before the implementation of the current licensing policy remain governed by their validly applicable copyright and licensing arrangements.

The adoption of CC BY 4.0 does not automatically change licenses previously granted under different terms.

Copyright and License Statement

Copyright © [Year], The Author(s).

The author(s) retain copyright and grant Jurnal MSA non-exclusive rights of first publication, dissemination, indexing, and preservation.

This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

https://creativecommons.org/licenses/by/4.0/

Most read articles by the same author(s)