Comparative analysis of Black-Scholes and GARCH models using collar strategy for hedging in telecommunication industry (Telkom, Xl, Indosat)

https://doi.org/10.35912/ijamis.v3i2.3334
Published: Aug 15, 2025

Abstract:

Purpose: This study examines the implementation of option contracts in the Black-Scholes model by comparing historical volatility and GARCH volatility using a collar strategy on TLKM, EXCL, and ISAT shares for the 2007–2024 period, aiming to determine the most appropriate model under crisis and normal conditions.

Research/methodology: The Black-Scholes model is applied with two volatility estimation methods historical and GARCH on options with 1-month and 3-month maturities, analyzed across crisis and non-crisis periods.

Results: For TLKM, with a 1-month maturity, GARCH outperformed historical volatility except during the 2008–2009 crisis; for 3 months, historical volatility outperformed in 2007, 2008–2009, and 2023–2024. For EXCL, historical volatility outperformed at 3 months in all conditions and at 1 month during crises; GARCH outperformed at 1 month in non-crisis periods. For ISAT, GARCH outperformed at 1 month except during the 2008–2009 crisis; historical volatility outperformed at 3 months during the non-crisis periods of 2007, 2023–2024, and the 2008–2009 crisis.

Conclusions: Performance varies by volatility method, maturity, and market condition. GARCH tends to perform better for short-term maturities in non-crisis periods, while historical volatility performs better for longer maturities and certain crisis periods.

Limitations: This study is limited to TLKM, EXCL, and ISAT stocks from 2007–2024, using only Black-Scholes and GARCH models with collar strategy, and may not generalize to other sectors or instruments.

Contribution: The study offers empirical evidence on optimal volatility modeling for hedging in Indonesia’s telecommunications sector.

Keywords:
1. Black-Scholes
2. Collar
3. GARCH
4. Option Contract
5. Stock
Authors:
1 . Abdul Mukti Soma
Telkom University, Bandung, Jawa Barat, Indonesia
2 . Victor Bastanta Sitepu
Telkom University, Bandung, Jawa Barat, Indonesia
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How to Cite
Soma, A. M., & Sitepu, V. B. (2025). Comparative analysis of Black-Scholes and GARCH models using collar strategy for hedging in telecommunication industry (Telkom, Xl, Indosat). International Journal of Accounting and Management Information Systems, 3(2), 137–155. https://doi.org/10.35912/ijamis.v3i2.3334
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Vol. 3 No. 2 (2025): August
Articles
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References

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    Budiarti, A., Isynuwardhana, D., & Hendratno. (2018). Imbal Hasil Kontrak Opsi Menggunakan Covered Call Writing Strategy dan Protective Put Buying Strategy. JRAK, 10(1), 16-21. doi:https://doi.org/10.23969/jrak.v10i1.1057

    El-Hassan, N., Hall, A., & Tulunay, I. (2021). Methods and Analysis of Collar Strategies. Journal of Applied Business and Economics, 23(8), 160-187. doi:https://doi.org/10.33423/jabe.v23i8.4882

    Engle, R. F., & Bollerslev, T. (1986). Modelling the Persistence of Conditional Variances. Econometric reviews, 5(1), 1-50. doi:https://doi.org/10.1080/07474938608800095

    Fajrina, N., Lubis, A., & Mustangin. (2024). Analisis Faktor Inflasi dan Suku Bunga Terhadap Volatilitas Harga Saham (Studi Kasus pada Perusahaan yang Terdaftar dalam Indeks LQ-45 di Bursa Efek Indonesia). Jurnal Akuntansi dan Keuangan Entitas, 4(1), 42-52.

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    Hardianti, N. I., & Widarjono, A. (2017). Dampak Penerbitan Sukuk dan Obligasi Konvensional Terhadap Return Saham Perusahaan di Indonesia. Jurnal Ekonomi & Keuangan Islam, 3(1), 43-51. doi:https://doi.org/10.20885/jeki.vol3.iss1.art6

    Hendrawan, R., & Arifin, Z. (2023). Comparison of Black-Scholes and GARCH Option Models on The Jakarta Islamic Index with Collar Strategy. Journal of Finance & Banking Review (JFBR), 7(4), 16-27. doi:https://doi.org/10.35609/jfbr.2023.7.4(2)

    Hendrawan, R., Laksana, G. T., & Aminah, W. (2020). Can The IDX Be Hegded?: Comparison of Black Scholes Option Model and Garch Option Model Using Long Strangle Strategy. Jurnal Manajemen Indonesia, 20(3), 252-259. doi:https://doi.org/10.25124/jmi.v20i3.3521

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    Irawan, W. O. (2017). Penentuan Harga Opsi dengan Model Black-Scholes Menggunakan Metode Beda Hingga Center Time Center Space (CTCS). EKSAKTA: Berkala Ilmiah Bidang MIPA, 18(2), 191-199. doi:https://doi.org/10.24036/eksakta/vol18-iss02/77

    Israelov, R., Klein, M., & Moore, H. (2017). Practical Applications of Risk and Return of Equity Index Collar Strategies. Practical Applications, 19(1), 1-5. doi:https://doi.org/10.3905/pa.2017.4.5.221

    Isynuwardhana, D., & Surur, G. N. I. (2018). Return Analysis on Contract Option Using Long Straddle Strategy and Short Straddle Strategy with Black Scholes. International Journal of Academic Research in Accounting, Finance and Management Sciences, 8(4), 16-20. doi:https://doi.org/10.6007/ijarafms/v8-i4/5181

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    Karagozoglu, A. K. (2022). Option Pricing Models: From Black-Scholes-Merton to Present. Journal of Derivatives, 29(4). doi:10.3905/jod.2022.1.158

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    Lindgren, J. (2023). A Generalized Model for Pricing Financial Derivatives Consistent with Efficient Markets Hypothesis—A Refinement of the Black-Scholes Model. Risks, 11(2), 1-5. doi:https://doi.org/10.3390/risks11020024

    Mahmood, S., Misra, P., Sun, H., Luqman, A., & Papa, A. (2024). Sustainable Infrastructure, Energy Projects, and Economic Growth: Mediating Role of Sustainable Supply Chain Management. Annals of operations research, 1-32. doi:https://doi.org/10.1007/s10479-023-05777-6

    Martin, V. L., Tang, C., & Yao, W. (2021). Forecasting the Volatility of Asset Returns: The Informational Gains from Option Prices. International Journal of Forecasting, 37(2), 862-880. doi:https://doi.org/10.1016/j.ijforecast.2020.09.012

    Mooy, M. N., Rusgiyono, A., & Rahmawati, R. (2017). Penentuan Harga Opsi Put dan Call Tipe Eropa Terhadap Saham Menggunakan Model Black-Scholes. Jurnal Gaussian, 6(3), 407-417. doi:https://doi.org/10.14710/j.gauss.6.3.407-417

    Naimy, V. Y., & Hayek, M. R. (2018). Modelling and predicting the Bitcoin volatility using GARCH models. International Journal of Mathematical Modelling and Numerical Optimisation, 8(3), 197-215. doi:https://doi.org/10.1504/IJMMNO.2018.088994

    Thoyibah, Q. A. y. P., & Sugiharti, L. (2022). The Effect of Telecommunication Infrastructure on Economic Growth in the Six ASEAN Countries. Media Trend, 17(1), 156-167. doi:https://doi.org/10.21107/mediatrend.v17i1.13640

    Widiarma, I. a., & Yulianto, A. E. (2023). The Effect of the Indihome Spin Off from PT Telkom Indonesia (Persero) and the Merger of Indihome with Telkomsel on TLKM Shares on the IDX and TLK Shares on the NYSE. Journal of Trends Economics and Accounting Research, 4(2), 487-497. doi:https://doi.org/10.47065/jtear.v4i2.1051

  1. Bi, Z., Yousuf, A., & Dash, M. (2014). A Study on Options Pricing Using GARCH and Black-Scholes-Merton Model. Asian Journal of Finance & Accounting, 6(1), 423-439. doi:https://doi.org/10.5296/ajfa.v6i1.4830
  2. Budiarti, A., Isynuwardhana, D., & Hendratno. (2018). Imbal Hasil Kontrak Opsi Menggunakan Covered Call Writing Strategy dan Protective Put Buying Strategy. JRAK, 10(1), 16-21. doi:https://doi.org/10.23969/jrak.v10i1.1057
  3. El-Hassan, N., Hall, A., & Tulunay, I. (2021). Methods and Analysis of Collar Strategies. Journal of Applied Business and Economics, 23(8), 160-187. doi:https://doi.org/10.33423/jabe.v23i8.4882
  4. Engle, R. F., & Bollerslev, T. (1986). Modelling the Persistence of Conditional Variances. Econometric reviews, 5(1), 1-50. doi:https://doi.org/10.1080/07474938608800095
  5. Fajrina, N., Lubis, A., & Mustangin. (2024). Analisis Faktor Inflasi dan Suku Bunga Terhadap Volatilitas Harga Saham (Studi Kasus pada Perusahaan yang Terdaftar dalam Indeks LQ-45 di Bursa Efek Indonesia). Jurnal Akuntansi dan Keuangan Entitas, 4(1), 42-52.
  6. Farahani, M. S., Babaei, S., & Esfahani, A. (2024). “Black-Scholes-Artificial Neural Network”: A Novel Option Pricing Model. International Journal of Financial, Accounting, and Management, 5(4), 475-509. doi:https://doi.org/10.35912/ijfam.v5i4.1684
  7. Gupta, A., & Mishra, R. (2024). A Comprehensive Study of Stock Market Volatility: Types, Determinants, and Measurement Methods. International Journal For Multidisciplinary Research, 6(6), 1-14. doi:http://dx.doi.org/10.36948/ijfmr.2024.v06i06.30054
  8. Hardianti, N. I., & Widarjono, A. (2017). Dampak Penerbitan Sukuk dan Obligasi Konvensional Terhadap Return Saham Perusahaan di Indonesia. Jurnal Ekonomi & Keuangan Islam, 3(1), 43-51. doi:https://doi.org/10.20885/jeki.vol3.iss1.art6
  9. Hendrawan, R., & Arifin, Z. (2023). Comparison of Black-Scholes and GARCH Option Models on The Jakarta Islamic Index with Collar Strategy. Journal of Finance & Banking Review (JFBR), 7(4), 16-27. doi:https://doi.org/10.35609/jfbr.2023.7.4(2)
  10. Hendrawan, R., Laksana, G. T., & Aminah, W. (2020). Can The IDX Be Hegded?: Comparison of Black Scholes Option Model and Garch Option Model Using Long Strangle Strategy. Jurnal Manajemen Indonesia, 20(3), 252-259. doi:https://doi.org/10.25124/jmi.v20i3.3521
  11. Hull, J. (2009). Options, Futures, and Other Derivatives 7th Edition. New Jersey: Pearson Education.
  12. Husnul, N., Setiyono, A., & Annasr, N. N. (2023). Pendidikan dan Pelatihan Pembuatan Makanan Tambahan pada Ibu Balita dan Kader Menuju Masyarakat Sadar Stunting di Kota Tasikmalaya. Jurnal Abdimas Kedokteran Dan Kesehatan, 1(1), 27-33. doi:https://doi.org/10.24853/jaras.1.1.27-33
  13. Irawan, W. O. (2017). Penentuan Harga Opsi dengan Model Black-Scholes Menggunakan Metode Beda Hingga Center Time Center Space (CTCS). EKSAKTA: Berkala Ilmiah Bidang MIPA, 18(2), 191-199. doi:https://doi.org/10.24036/eksakta/vol18-iss02/77
  14. Israelov, R., Klein, M., & Moore, H. (2017). Practical Applications of Risk and Return of Equity Index Collar Strategies. Practical Applications, 19(1), 1-5. doi:https://doi.org/10.3905/pa.2017.4.5.221
  15. Isynuwardhana, D., & Surur, G. N. I. (2018). Return Analysis on Contract Option Using Long Straddle Strategy and Short Straddle Strategy with Black Scholes. International Journal of Academic Research in Accounting, Finance and Management Sciences, 8(4), 16-20. doi:https://doi.org/10.6007/ijarafms/v8-i4/5181
  16. Jain, R. K. (2001). Putting Volatility to Work. New York: Active Trader.
  17. Karagozoglu, A. K. (2022). Option Pricing Models: From Black-Scholes-Merton to Present. Journal of Derivatives, 29(4). doi:10.3905/jod.2022.1.158
  18. Li, P., & Yang, J. (2017). Pricing Collar Options with Stochastic Volatility. Discrete Dynamics in Nature and Society, 1-7. doi:https://doi.org/10.1155/2017/9673630
  19. Lindgren, J. (2023). A Generalized Model for Pricing Financial Derivatives Consistent with Efficient Markets Hypothesis—A Refinement of the Black-Scholes Model. Risks, 11(2), 1-5. doi:https://doi.org/10.3390/risks11020024
  20. Mahmood, S., Misra, P., Sun, H., Luqman, A., & Papa, A. (2024). Sustainable Infrastructure, Energy Projects, and Economic Growth: Mediating Role of Sustainable Supply Chain Management. Annals of operations research, 1-32. doi:https://doi.org/10.1007/s10479-023-05777-6
  21. Martin, V. L., Tang, C., & Yao, W. (2021). Forecasting the Volatility of Asset Returns: The Informational Gains from Option Prices. International Journal of Forecasting, 37(2), 862-880. doi:https://doi.org/10.1016/j.ijforecast.2020.09.012
  22. Mooy, M. N., Rusgiyono, A., & Rahmawati, R. (2017). Penentuan Harga Opsi Put dan Call Tipe Eropa Terhadap Saham Menggunakan Model Black-Scholes. Jurnal Gaussian, 6(3), 407-417. doi:https://doi.org/10.14710/j.gauss.6.3.407-417
  23. Naimy, V. Y., & Hayek, M. R. (2018). Modelling and predicting the Bitcoin volatility using GARCH models. International Journal of Mathematical Modelling and Numerical Optimisation, 8(3), 197-215. doi:https://doi.org/10.1504/IJMMNO.2018.088994
  24. Thoyibah, Q. A. y. P., & Sugiharti, L. (2022). The Effect of Telecommunication Infrastructure on Economic Growth in the Six ASEAN Countries. Media Trend, 17(1), 156-167. doi:https://doi.org/10.21107/mediatrend.v17i1.13640
  25. Widiarma, I. a., & Yulianto, A. E. (2023). The Effect of the Indihome Spin Off from PT Telkom Indonesia (Persero) and the Merger of Indihome with Telkomsel on TLKM Shares on the IDX and TLK Shares on the NYSE. Journal of Trends Economics and Accounting Research, 4(2), 487-497. doi:https://doi.org/10.47065/jtear.v4i2.1051