Perhitungan harga opsi Asia dengan model jump diffusion menggunakan Monte Carlo antithetic variates dan control variates = Asian option pricing with jump diffusion model using Monte Carlo antithetic variates and control variates

Wijaya, Angeline Putri (2024) Perhitungan harga opsi Asia dengan model jump diffusion menggunakan Monte Carlo antithetic variates dan control variates = Asian option pricing with jump diffusion model using Monte Carlo antithetic variates and control variates. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Opsi adalah sebuah instrumen keuangan derivatif yang berguna sebagai alat investasi dan perlindungan dalam dunia keuangan. Opsi Asia adalah salah satu contoh dari opsi eksotis, di mana nilainya bergantung pada rata-rata harga aset dasar selama masa kontrak. Simulasi Monte Carlo (MCS) adalah salah satu metode numerik yang fleksibel dan dapat digunakan untuk valuasi harga opsi Asia yang bersifat path-dependent. Dalam penelitian ini, akan diterapkan dua teknik reduksi variansi untuk meningkatkan efisiensi MCS, yaitu antithetic variates dan control variates. Fokus utama penelitian ini adalah menguji model jump diffusion untuk menetapkan harga opsi Asia aritmatika dengan minyak WTI sebagai aset dasar. Dari tiga puluh dua valuasi opsi Asia yang dilakukan, hasil menunjukkan bahwa model jump diffusion belum berhasil mengungguli gerak Brownian Geometrik melalui antithetic variates. Meskipun demikian, dengan menerapkan control variates, model jump diffusion menunjukkan performa yang lebih baik. Dalam konteks perhitungan harga opsi Asia, control variates memberikan performa yang lebih baik dibandingkan dengan antithetic variates dari segi akurasi dan pengurangan variansi, meskipun antithetic variates memiliki keunggulan dalam waktu komputasi yang lebih cepat. Analisis juga menunjukkan bahwa opsi deep in-the-money memberikan galat yang lebih besar dibandingkan dengan opsi in-the-money, sementara opsi deep out-of-the-money memberikan galat yang lebih kecil dibandingkan dengan opsi out-of-the-money. Hal ini menunjukkan bahwa tingkat moneyness mempengaruhi akurasi hasil perhitungan opsi Asia. / Options are financial derivatives valuable for investment and risk management in the financial world. Asian options, which are classified as exotic options, are based on the average price of the underlying asset over the length of the contract. One particularly powerful numerical technique for valuing path-dependent Asian options is Monte Carlo simulation (MCS). In order to enhance Monte Carlo simulation performance, two variance reduction techniques—antithetic variates and control variates—will be applied in this work. The main purpose of this research is to evaluate the jump diffusion model's performance in estimating the arithmetic Asian option prices. According to the findings of thirty-two Asian option valuations, the jump diffusion model has not outperformed the Geometric Brownian Motion through antithetic variates. Nevertheless, the jump diffusion model performs better by using control variates. While antithetic variates have the advantage of faster computational time, control variates perform better in terms of accuracy and variance reduction when it comes to Asian option pricing. Additionally, the study shows that deep out-of-the-money options have smaller errors than out-of-the-money options, while deep in-the-money options have larger errors than in-the-money options. This implies that Asian option pricing computations' accuracy is influenced by the option moneyness level.

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