Option Pricing Using The Partial Taylor Series Expansion Method: A Case Study of Blue-Chip Stocks on The Indonesia Stock Exchange

Abstract

The Indonesian capital market is characterized by dynamic stock price volatility, which directly affects the value of derivative instruments, particularly stock options. Accurate option pricing is essential for supporting investment decision-making and risk management. The Black–Scholes model is a classical and widely used framework for option pricing; however, its assumption of constant volatility often fails to reflect actual market conditions. Therefore, this study aims to apply the Partial Taylor Series Expansion (PTSE) method as an alternative approximation approach and to evaluate its accuracy relative to the analytical Black–Scholes solution. This study adopts a quantitative approach using a blue-chip stock PT. XXXX listed on the Indonesia Stock Exchange during the period 2019–2024. Model parameters are determined based on historical stock price data, the risk-free interest rate, and historical volatility. European stock option prices are calculated using both the Black–Scholes model and the PTSE method and are compared using Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). In addition, sensitivity analysis is conducted to examine the effects of volatility and time to maturity on option price differences. The results indicate that the PTSE method produces option price estimates with relatively small errors and a stable convergence pattern toward the Black–Scholes model, suggesting that PTSE is a practical and efficient approximation approach for pricing European stock options in the Indonesian capital market.