Pricing European Call Options on LQ45 Stocks under Transaction Costs: A Barles-Soner-GARCH Approach
Abstract
This study prices European call options on 27 constituent-verified LQ45 stocks (February 2022-December 2025) with a Barles-Soner-GARCH framework benchmarked against Black-Scholes-GARCH. The 27 names are the survivors of 72 tickers screened against every official constituent evaluation in the window, so the panel is by construction the exchange's most persistently liquid segment and the figures below are conservative for that reason. Stock-level GARCH (1,1) forecasts supply the volatility inputs for 1,620 scenarios spanning moneyness, maturity and proportional transaction costs. At zero cost the finite-difference solver reproduces the analytical benchmark to a 0.10% mean relative error, and grid refinement confirms this is not mesh-specific. Because the nonlinear correction is non-negative by construction, a positive premium is structural rather than an empirical finding, so the informative quantities are its magnitude and cross-sectional pattern. The premium rises from 3.02% of spot at a cost of 0.005 to 7.51% at 0.020, but decomposing observable Indonesian trading costs places the representative one-way cost between 0.00250 and 0.00862, which puts the practically relevant premium nearer 1.51%-4.39% of spot and identifies 0.020 as a stress scenario. The premium concentrates in longer-maturity, high-gamma contracts on high-volatility stocks.
Keywords
Full Text:
PDFReferences
R. M. Ponziani, “The Modeling the Returns Volatility of Indonesian Stock Indices: The Case of SRI-KEHATI and LQ45,” Jurnal Ekonomi Modernisasi, vol. 18, no. 1, pp. 13–21, 2022, https://doi.org/10.21067/jem.v18i1.6411.
F. Black and M. Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, vol. 81, no. 3, pp. 637–654, 1973, https://doi.org/10.1086/260062.
R. C. Merton, “Theory of Rational Option Pricing,” The Bell Journal of Economics and Management Science, vol. 4, no. 1, pp. 141–183, 1973, https://doi.org/10.2307/3003143.
J.-P. Chavas, J. Li, and L. Wang, “Option Pricing Revisited: The Role of Price Volatility and Dynamics,” Journal of Commodity Markets, vol. 33, 2024, https://doi.org/10.1016/j.jcomm.2023.100381.
X.-J. He and S. Lin, “A Fractional Black-Scholes Model with Stochastic Volatility and European Option Pricing,” Expert Syst. Appl., vol. 178, 2021, https://doi.org/10.1016/j.eswa.2021.114983.
T. Wang, S. Cheng, F. Yin, and M. Yu, “Overnight Volatility, Realized Volatility, and Option Pricing,” Journal of Futures Markets, vol. 42, no. 7, pp. 1264–1283, 2022, https://doi.org/10.1002/fut.22330.
M. Escobar-Anel, J. Rastegari, and L. Stentoft, “Option Pricing with Conditional GARCH Models,” Eur. J. Oper. Res., vol. 289, no. 1, pp. 350–363, 2021, https://doi.org/10.1016/j.ejor.2020.07.002.
D. H. Oh and Y.-H. Park, “GARCH Option Pricing with Volatility Derivatives,” J. Bank. Financ., vol. 146, 2023, https://doi.org/10.1016/j.jbankfin.2022.106718.
Z. Fang and J.-Y. Han, “Realized GARCH Model in Volatility Forecasting and Option Pricing,” Comput. Econ., vol. 66, no. 5, pp. 3637–3657, 2025, https://doi.org/10.1007/s10614-024-10826-8.
M. Escobar-Anel, L. Stentoft, and X. Ye, “The Benefits of Returns and Options in the Estimation of GARCH Models: A Heston-Nandi GARCH Insight,” Econom. Stat., vol. 36, pp. 1–18, 2025, https://doi.org/10.1016/j.ecosta.2022.12.001.
M. Escobar-Anel, L. Stentoft, and X. Ye, “Not All VIXs Are (Informationally) Equal: Evidence from Affine GARCH Option Pricing Models,” Financ. Res. Lett., vol. 69, 2024, doi: 10.1016/j.frl.2024.106053.
C. Chorro and R. H. Fanirisoa Zazaravaka, “Discriminating Between GARCH Models for Option Pricing by Their Ability to Compute Accurate VIX Measures,” Journal of Financial Econometrics, vol. 20, no. 5, pp. 902–941, 2022, https://doi.org/10.1093/jjfinec/nbaa042.
N. Zulfiqar and S. Gulzar, “Implied Volatility Estimation of Bitcoin Options and the Stylized Facts of Option Pricing,” Financial Innovation, vol. 7, no. 1, 2021, https://doi.org/10.1186/s40854-021-00280-y.
T. Pang and Y. Zhao, “On GARCH and Autoregressive Stochastic Volatility Approaches for Market Calibration and Option Pricing,” Risks, vol. 13, no. 2, 2025, https://doi.org/10.3390/risks13020031.
P. J. Venter and E. Mare, “GARCH Option Pricing and Implied FX Volatility Indices,” Studies in Economics and Econometrics, vol. 45, no. 1, pp. 42–52, 2021, https://doi.org/10.1080/03796205.2021.1956170.
P. J. Venter and E. Mare, “Univariate and Multivariate GARCH Models Applied to Bitcoin Futures Option Pricing,” Journal of Risk and Financial Management, vol. 14, no. 6, 2021, https://doi.org/10.3390/jrfm14060261.
G. Barles and H. M. Soner, “Option Pricing with Transaction Costs and a Nonlinear Black-Scholes Equation,” Finance and Stochastics, vol. 2, no. 4, pp. 369–397, 1998, doi: 10.1007/s007800050046.
H. E. Leland, “Option Pricing and Replication with Transactions Costs,” J. Finance, vol. 40, no. 5, pp. 1283–1301, 1985, https://doi.org/10.1111/j.1540-6261.1985.tb02383.x.
D. M. F. Noor and R. Artiono, “Numerical Pricing of European Options under Proportional Transaction Costs: A Semi-Discretization Approach to the Nonlinear Barles-Soner Model,” ZERO: Jurnal Sains, Matematika dan Terapan, vol. 10, no. 1, 2026, https://doi.org/10.30829/zero.v10i1.28084.
M. Taufik and R. Artiono, “The Valuation of European Options with Transaction Costs Using the Barles-Soner Model,” ZERO: Jurnal Sains, Matematika dan Terapan, vol. 9, no. 3, 2025, https://doi.org/10.30829/zero.v9i3.27702.
R. Company, L. Jódar, and J.-R. Pintos, “Consistent Stable Difference Schemes for Nonlinear Black-Scholes Equations Modelling Option Pricing with Transaction Costs,” ESAIM: Mathematical Modelling and Numerical Analysis, vol. 43, no. 6, pp. 1045–1061, 2009, https://doi.org/10.1051/m2an/2009014.
J. de Frutos and V. Gatón, “A Pseudospectral Method for Option Pricing with Transaction Costs under Exponential Utility,” J. Comput. Appl. Math., vol. 394, 2021, https://doi.org/10.1016/j.cam.2021.113541.
P. Pálvóra and D. Ševčovič, “Utility Indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation,” Journal of Risk and Financial Management, vol. 14, no. 9, 2021, https://doi.org/10.3390/jrfm14090399.
M. Rezaei, A. R. Yazdanian, A. Ashrafi, and S. M. Mahmoudi, “Numerically Pricing Nonlinear Time-Fractional Black-Scholes Equation with Time-Dependent Parameters Under Transaction Costs,” Comput. Econ., vol. 60, no. 1, pp. 243–280, 2021, https://doi.org/10.1007/s10614-021-10148-z.
T. Saeed, J. Hussain, and S. Rafique, “Option Pricing under Stochastic Interest Rates and Transaction Costs Using Physics-Informed Neural Networks,” Examples and Counterexamples, vol. 10, 2026, https://doi.org/10.1016/j.exco.2026.100227.
M. R. Shakeel, S. Yadav, and M. Ahmad, “Option Pricing under Regime-Switching Jump-Diffusion Dynamics with Transaction Costs: A Neural SDE Approach,” Review of Derivatives Research, vol. 29, no. 1, 2026, https://doi.org/10.1007/s11147-026-09238-7.
D. Yan, “A Comprehensive Study of Option Pricing with Transaction Costs,” Bull. Aust. Math. Soc., vol. 106, no. 3, pp. 522–524, 2022, https://doi.org/10.1017/S0004972722000740.
X. Cai and Y. Wang, “A Novel Fourth-Order Finite Difference Scheme for European Option Pricing in the Time-Fractional Black-Scholes Model,” Mathematics, vol. 12, no. 21, 2024, https://doi.org/10.3390/math12213343.
Y. Feng, X. Zhang, Y. Chen, and L. Wei, “A Compact Finite Difference Scheme for Solving Fractional Black-Scholes Option Pricing Model,” J. Inequal. Appl., vol. 2025, no. 1, 2025, https://doi.org/10.1186/s13660-025-03261-2.
P. Roul and V. M. K. P. Goura, “A Compact Finite Difference Scheme for Fractional Black-Scholes Option Pricing Model,” Applied Numerical Mathematics, vol. 166, pp. 40–60, 2021, https://doi.org/10.1016/j.apnum.2021.03.017.
B. R. I. D. Sekuritas, “Memahami Biaya Transaksi Saham Sebelum Mulai Investasi,” 2025.
R. Roll, “A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market,” J. Finance, vol. 39, no. 4, pp. 1127–1139, 1984, https://doi.org/10.1111/j.1540-6261.1984.tb03897.x.
L. Harris, “Statistical Properties of the Roll Serial Covariance Bid/Ask Spread Estimator,” J. Finance, vol. 45, no. 2, pp. 579–590, 1990, https://doi.org/10.1111/j.1540-6261.1990.tb03704.x.
DOI: http://dx.doi.org/10.30829/zero.v10i2.31303
Refbacks
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.