Perbandingan Metode Monte Carlo Antithetic Variate dan Control Variate dalam Penentuan Harga Opsi Barrier Knock-Out

Chatarina Enny Murwaningtyas; William Saputra Haryono; Maria Andriani Uge; Tedi Kristofel

doi:10.37905/euler.v12i1.25128

Perbandingan Metode Monte Carlo Antithetic Variate dan Control Variate dalam Penentuan Harga Opsi Barrier Knock-Out

Chatarina Enny Murwaningtyas, William Saputra Haryono, Maria Andriani Uge, Tedi Kristofel

Abstract

This study aims to examine the effectiveness of the Monte Carlo antithetic variate and control variate methods in pricing knock-out barrier options compared to the standard Monte Carlo method. The main problem in barrier option pricing is the high variance of estimates, which can reduce the accuracy and efficiency of results. The standard Monte Carlo method often requires a very large number of simulations to achieve stable results, which is computationally inefficient. To address this issue, this study employs variance reduction techniques, antithetic variate, and control variate. The findings indicate that both methods offer higher accuracy in price estimation compared to the standard Monte Carlo method. Further analysis reveals that the control variate method is more effective for pricing up and out barrier call options and down and out barrier call options, while the antithetic variate method excels in pricing up and out barrier put options and down and out barrier put options. This study underscores the importance of selecting the appropriate method according to the type of option involved to achieve accurate and efficient estimations.

Keywords

Knock-Out Barrier Options; Monte Carlo; Antithetic Variate; Control Variate

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References

D. H. Vo, S. Van Huynh, A. T. Vo, and D. T. T. Ha, “The Importance of the Financial Derivatives Markets to Economic Development in the World’s Four Major Economies,” Journal of Risk and Financial Management, vol. 12, no. 1, Mar. 2019, doi: https://doi.org/10.3390/jrfm12010035.

P. Wilmott, S. Howison, and J. Dewynne, The Mathematics of Financial Derivatives. 1995. doi: https://doi.org/10.1017/cbo9780511812545.

P. Wilmott, Introduces Quantitative Finance. in The Wiley Finance Series. Wiley, 2013.

H. Brown, D. Hobson, and L. C. G. Rogers, “Robust Hedging Of Barrier Options,” 2001. doi: https://doi.org/10.1111/1467-9965.00116.

J. C. Hull and S. Basu, Options, futures, and other derivatives. India: Pearson Education, 2012.

P. Glasserman, Monte Carlo Methods in Financial Engineering. in Stochastic Modelling and Applied Probability. New York: Springer, 2013.

D. J. Higham, An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation, no. v. 13. in An introduction to financial option valuation: mathematics, stochastics and computation. Cambridge University Press, 2004.

C. F. Ivascu, “Option pricing using Machine Learning,” Expert Syst Appl, vol. 163, Jan. 2021, doi: https://doi.org/10.1016/j.eswa.2020.113799.

W. Li, “Application of Machine Learning in Option Pricing: A Review,”

in 2022 7th International Conference on Social Sciences and Economic Development (ICSSED 2022), Atlantis Press, 2022, pp. 209–214. doi: https://doi.org/10.2991/aebmr.k.220405.035.

L. Lin, M. Wang, H. Cheng, R. Liu, and F. Chen, “OptionNet: A multiscale residual deep learning model with confidence interval to predict option price,” Journal of Finance and Data Science, vol. 9, Nov. 2023, doi: https://doi.org/10.1016/j.jfds.2023.100105.

A. Brini and J. Lenz, “Pricing cryptocurrency options with machine learning regression for handling market volatility,” Econ Model, vol. 136, Jul. 2024, doi: https://doi.org/10.1016/j.econmod.2024.106752.

Y. Li and K. Yan, “Prediction of Barrier Option Price Based on Antithetic Monte Carlo and Machine Learning Methods,” Cloud Computing and Data Science, pp. 77–86, Jan. 2023, doi: https://doi.org/10.37256/ccds.4120232110.

N. P. Kurniawati, Y. Yundari, and S. W. Rizki, “Analisis Harga Opsi

Beli Tipe Eropa dengan Metode Antithetic Variate dari Monte Carlo,” Jurnal EurekaMatika, vol. 10, no. 1, pp. 53–60, 2022, doi: https://doi.org/10.17509/jem.v10i1.47673.

F. Zubedi, N. Achmad, S. L. Mahmud, and R. Mowuu, “Penentuan Harga Beli Opsi Asia Menggunakan Monte Carlo-Antithetic Variate dan Monte CarloControl,” Euler: Jurnal Ilmiah Matematika, Sains dan Teknologi, vol. 10, no. 1, pp. 7–14, 2022, doi: https://doi.org/10.37905/euler.v10i1.12055.

N. Wati, K. Dharmawan, and K. Sari, “Perbandingan kekonvergenan metode Conditional Monte Carlo dan antithetic variate dalam menentukan harga opsi call tipe Barrier,” E-Jurnal Matematika, vol. 7, no. 3, pp. 271–277, 2018, doi: https://doi.org/10.24843/MTK.2018.v07.i03.p214.

L. Putri, K. Dharmawan, and I. W. Sumarjaya, “Penentuan Harga Jual Opsi Barrier Tipe Eropa Dengan Metode Antithetic Variate Pada Simulasi Monte Carlo,” E-Jurnal Matematika, vol. 7, no. 2, pp. 71–78, 2018, doi: https://doi.org/10.24843/MTK.2018.v07.i02.p187.

R. B. Silalahi, D. C. Lesmana, and R. Budiarti, “Determining The Value of Double Barrier Option Using Standard Monte Carlo, Antithetic Variate, and Control Variate Methods,” Barekeng: Jurnal Ilmu Matematika dan Terapan, vol. 17, no. 2, pp. 1017–1026, 2023, doi: https://doi.org/10.30598/barekengvol17iss2pp1017-1026.

F. Black and M. Scholes, “The pricing of options and corporate liabilities,” J Polit Econ, pp. 637–654, 1973.

M. Broadie, P. Glasserman, and S. Kou, “A Continuity Correction for Discrete Barrier Options,” Math Financ, vol. 7, no. 4, pp. 325–349, 1997, doi: https://doi.org/10.1111/1467-9965.00035.

DOI: https://doi.org/10.37905/euler.v12i1.25128