The Valuation of European Options with Transaction Costs Using the Barles-Soner Model

Taufik, Muchammad (Mathemathics Department, Universitas Negeri Surabaya, Sidoarjo, 61257, Indonesia)
Artiono, Rudianto (Mathemathics Department, Universitas Negeri Surabaya, Surabaya, 60241, Indonesia)

Zero : Jurnal Sains, Matematika, dan Terapan
Vol 9, No 3 (2025): Zero: Jurnal Sains Matematika dan Terapan

This study discusses the pricing of European call options by considering transaction costs using the Barles-Soner model. The method used in this study is an analytical and asymptotic approach based on literature studies. Stock and option price data were obtained from Yahoo Finance, while the risk-free interest rate was taken from the Federal Reserve Bank of St. Louis. Volatility was calculated based on historical stock return data, while transaction costs and risk aversion parameters were determined based on previous studies. The Barles-Soner model introduces non-linear effective volatility, which is estimated using an asymptotic approach to obtain effective volatility. The option price calculated using the Barles-Soner model is , higher than the option price using the Black-Scholes model of , with a difference of . These results confirm that transaction costs have a significant effect on option prices. Therefore, the Barles-Soner model is more comprehensive in calculating stock option prices than the Black-Scholes model.