Electronic Theses and Dissertation

Model Black-Scholes masih menjadi standar industri dalam penilaian opsi, namun keterbatasan asumsi distribusinya memunculkan pertanyaan mengenai keunggulan model-model alternatif. Penelitian ini bertujuan membandingkan akurasi model Black-Scholes, Bachelier, simulasi Monte Carlo Jump-Diffusion, dan Artificial Neural Network dalam memprediksi harga opsi beli tipe Eropa pada indeks S&P 500. Data yang digunakan adalah data sekunder opsi S&P 500 harian periode 2019– 2025. Akurasi setiap model diukur dengan MAE, RMSE, dan MAPE, sedangkan signifikansi perbedaannya diuji dengan uji Diebold-Mariano. Hasil penelitian menunjukkan bahwa model Bachelier signifikan lebih akurat daripada Black- Scholes, sementara Black-Scholes, Bachelier, dan Artificial Neural Network masing-masing signifikan lebih akurat daripada simulasi Monte Carlo yang menempati akurasi terendah. Meskipun Artificial Neural Network mencatat kesalahan deskriptif terendah, keunggulannya atas Black-Scholes dan Bachelier tidak signifikan secara statistik pada level agregat. Tidak ada model yang unggul di seluruh kondisi karena akurasi terspesialisasi menurut moneyness dan waktu jatuh tempo. Di antara estimator volatilitas yang diuji, EGARCH menghasilkan akurasi tertinggi karena mampu menangkap leverage effect. Berdasarkan dekomposisi uji per kategori, model Bachelier dengan input EGARCH unggul pada kategori terbanyak dan tidak pernah kalah dari Black-Scholes sehingga layak dijadikan sebagai acuan awal. Pemilihan model penilaian opsi sebaiknya mempertimbangkan karakteristik kontrak dan kondisi pasar, bukan hanya peringkat akurasi agregat.
Kata kunci: penilaian opsi, Black-Scholes, Bachelier, simulasi Monte Carlo, Artificial Neural Network

The Black-Scholes model remains the industry standard for option pricing, yet the limitations of its distributional assumptions raise questions about the superiority of alternative models. This study compares the accuracy of the Black-Scholes, Bachelier, Monte Carlo Jump-Diffusion, and Artificial Neural Network models in predicting European call option prices on the S&P 500 index. It uses secondary data on daily S&P 500 options over the 2019–2025 period. Accuracy is measured using MAE, RMSE, and MAPE, while the significance of the differences is tested using the Diebold-Mariano test. The results show that Bachelier is significantly more accurate than Black-Scholes, while Black-Scholes, Bachelier, and Artificial Neural Network are each significantly more accurate than Monte Carlo simulation, which ranks lowest. Although Artificial Neural Network records the lowest descriptive errors, its advantage over Black-Scholes and Bachelier is not statistically significant at the aggregate level. No single model is superior across all conditions, as accuracy specializes by moneyness and time to maturity. Among the volatility estimators tested, EGARCH yields the highest accuracy owing to its ability to capture the leverage effect. Based on the category-level decomposition, Bachelier with EGARCH inputs wins in the most categories and never loses to Black-Scholes, making it worthy of being used as an initial reference. Model selection should therefore consider contract characteristics, not aggregate accuracy rankings alone. Keywords: option pricing, Black-Scholes, Bachelier, Monte Carlo simulation, Artificial Neural Network