CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI

Sobol and GJR-GARCH for Dominant Factors of European Option Prices in Blue-Chip Index Constituent Stocks

Nathania Azzah Mu’azara (Mathematics Department, Universitas Negeri Surabaya)
Rudianto Artiono (Mathematics Department, Universitas Negeri Surabaya)



Article Info

Publish Date
30 Nov 2026

Abstract

Conditional volatility-based option pricing research generally emphasizes improving volatility inputs, but has not yet fully explained the relative contribution of each parameter to variation in simulated option-pricing responses for Indonesian index stocks. This study integrates BlackScholes, GJR-GARCH asymmetric volatility, and Sobol global sensitivity analysis to identify dominant factors in a model-generated European call-option response for verified constituents of an Indonesian blue-chip index, denoted Index X. The sample consists of 19 constituents that remained consistent from February 2022 to December 2025. Logarithmic returns are tested for stationarity and ARCH effects, conditional volatility is estimated using GJR-GARCH(1,1), and the BlackScholes response is evaluated with five independently and uniformly distributed inputs: moneyness, maturity, risk-free rate, volatility multiplier, and proportional transaction cost. The results show that all returns are stationary and most stocks exhibit significant ARCH effects. Under the baseline domain, maturity and moneyness are the leading factors, while the volatility multiplier is secondary and the risk-free rate and transaction cost have smaller contributions. The ranking remains contract-dominated under a wider scenario domain and under a Student-t innovation check, although the magnitudes and ordering of maturity and moneyness can change. The contribution of this research is sensitivity decomposition of a specified BlackScholes response with a GJR-GARCH-based volatility input, not evidence of improved pricing accuracy against observed option prices. Issuer and index identities are masked in the manuscript to prevent issuer-specific model outputs from being misconstrued as investment recommendations or comparative assessments; a confidential identity crosswalk is retained for editorial verification.

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Journal Info

Abbrev

Math

Publisher

Subject

Mathematics

Description

Jurnal CAUCHY secara berkala terbit dua (2) kali dalam setahun. Redaksi menerima tulisan ilmiah hasil penelitian, kajian kepustakaan, analisis dan pemecahan permasalahan di bidang Matematika (Aljabar, Analisis, Statistika, Komputasi, dan Terapan). Naskah yang diterima akan dikilas (review) oleh ...