Numerical Pricing of European Options under Proportional Transaction Costs: A Semi-Discretization Approach to the Nonlinear Barles-Soner Model

Noor, Dwi Maya Firanti (Mathematics Department, Universitas Negeri Surabaya, Surabaya, 60231, Indonesia)
Artiono, Rudianto (Mathematics Department, Universitas Negeri Surabaya, Surabaya, 60231, Indonesia)

Zero : Jurnal Sains, Matematika, dan Terapan
Vol 10, No 1 (2026): Zero: Jurnal Sains Matematika dan Terapan

The classical Black–Scholes model assumes a frictionless market, which often leads to the undervaluation of option premiums when transaction costs are present. This study prices European call options under proportional transaction costs using the nonlinear Barles–Soner framework and a semi-discretization–based numerical approach. Using historical stock data from PT XYZ (an anonymized Indonesian equity), the results show that transaction costs significantly increase effective volatility and generate systematic deviations from classical Black–Scholes prices. In particular, option premiums increase by IDR 392.33 and IDR 776.66 for transaction cost parameters of 0.015 and 0.030, respectively, compared with the frictionless benchmark. These findings confirm that ignoring transaction costs leads to substantial underpricing and that the proposed framework provides a more realistic and conservative valuation for hedging and risk management in emerging markets.