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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Aditama, Muhammad Iqbal
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Mathematics

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Numerical Pricing of European Stock Options Using Black-Scholes Interval Model Aditama, Muhammad Iqbal; Artiono, Rudianto
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.40272

Abstract

This study presents the numerical implementation of the Black-Scholes interval model for determining the price of European call options under parameter uncertainty. Unlike the classic Black-Scholes model, which assumes fixed volatility and risk-free interest rates, this study represents both parameters as limited intervals constructed based on historical data. Daily stock closing prices obtained from Yahoo Finance and risk-free interest rate data from the Federal Reserve Bank of St. Louis were used to define the parameter ranges. The interval Black-Scholes model was discretized in the asset price and time domains and solved numerically by formulating an optimization problem that minimizes the residual error of the interval partial differential equation with terminal payoff constraints. The numerical solution produces lower and upper bounds for option prices in the specified domain. Simulation results show that classic Black-Scholes option prices lie within the calculated interval price bounds, demonstrating numerical consistency between the deterministic and interval formulations.This study provides a structured numerical case study showing how the Black-Scholes interval model can be implemented to generate option price bounds under bounded parameter uncertainty
Co-Authors RUDIANTO ARTIONO, RUDIANTO