Judul: A Comparison between Implicit and Crank Nicolson Finite Difference Method for Pricing European Options
Abstrak: Pada karya ilmiah ini, dibahas perbandingan dua metode beda hingga dalam menentukan harga opsi, yaitu metode beda hingga implisit dan metode beda hingga Crank-Nicolson. Kedua metode tersebut dilihat perbandingannya dari segi akurasi terhadap nilai analitik model Black-Scholes dan efisiensi waktu komputasinya. Metode beda hingga implisit adalah metode yang digunakan untuk mencari solusi numerik dari persamaan diferensial parsial dengan menggunakan aproksimasi maju, sedangkan metode beda hingga Crank-Nicolson menggunakan rata-rata skema dari metode eksplisit dan implisit. Kedua metode tersebut diterapkan untuk mencari harga opsi Eropa dengan underlying asset berupa saham GOOG. Metode beda hingga Crank-Nicolson memiliki akurasi yang lebih tinggi daripada metode beda hingga implisit. Lalu, untuk penghitungan waktu komputasi, metode beda hingga implisit lebih efisien dibandingkan metode beda hingga Crank-Nicolson., In this thesis, a comparison of two finite difference methods for determining option prices is discussed, there is the implicit finite difference method and the Crank-Nicolson finite difference method. These two methods are compared in terms of both the accuracy of the analytical value of the Black-Scholes model and the efficiency of computing time. The implicit finite difference method is employed to find numerical solutions to partial differential equations using a forward approximation, while the Crank-Nicolson finite difference method utilizes an average scheme of the explicit and implicit methods. Both approaches are applied to calculate European option prices with the underlying asset represented by GOOG shares. The Crank-Nicolson finite difference method demonstrates higher accuracy compared to the implicit finite difference method. However, when considering computing time, the implicit finite difference method proves to be more efficient than the Crank-Nicolson finite difference method.
Keyword: Metode beda hingga Crank-Nicolson, Metode beda hingga implisit, Model Black-Scholes, Opsi Eropa, Black-Scholes model, Crank-Nicolson finite difference method, European option, Implicit finite difference method

Judul: European Option Pricing Using the Monte Carlo Method and the Finite Difference Method
Abstrak: Harga opsi Eropa umumnya dihitung menggunakan model Black-Scholes. Model ini dapat digunakan ketika asumsinya terpenuhi. Perdagangan opsi pada kenyataannya tidak memenuhi beberapa asumsi, sehingga model Black-Scholes tidak dapat memberikan solusi analitik untuk harga opsi. Hal ini menjadi alasan dibutuhkannya metode numerik untuk menghitung harga opsi Eropa. Pada penelitian ini digunakan dua metode numerik, yaitu metode Monte Carlo yang menghitung harga opsi dengan melakukan simulasi harga saham dan metode beda hingga yang melakukan diskretisasi pada persamaan diferensial parsial. Karya ilmiah ini memeriksa kekonvergenan untuk tiap metode. Selanjutnya, diperiksa pengaruh dari beberapa parameter terhadap harga opsi menggunakan metode beda hingga. Waktu jatuh tempo opsi dengan harga opsi memiliki hubungan yang berbeda untuk kondisi tertentu dan volatilitas harga saham berbanding lurus dengan harga opsi., European option prices are generally calculated using the Black-Scholes model. This model can be used when the assumptions are fulfilled. In fact, options trading does not fulfill several assumptions so the Black-Scholes model cannot provide an analytical solution for option prices. This is the reason for the need of numerical methods to calculate European option prices. This study uses numerical methods such as the Monte Carlo method which calculates option prices by simulating stock prices and the finite difference method which performs discretization on partial differential equations. This paper examines the convergence for each method. Next, we examine the effect of several parameters on the option price using the finite difference method. The expiration time of the option and the option price has a different relationship for certain conditions and the volatility of the stock price is directly proportional to the option price.
Keyword: European option, finite difference method, Monte Carlo method, option

Judul: Isolation and Characterization of Protease Keratinolytic Enzyme in Water Monitor Lizard Intestine.
Abstrak: Protease enzyme isolated from mucosa layer in intestine water monitor lizard (Varanus salvator) showed proteolytic activity. Therefore, the purpose of this research was to isolate and characterize of protease produced by water monitor lizard intestine. The intestine mucous layer of water monitor lizard (2%) was dissolved in 50mM buffer phosphate pH 7,0, then centrifuged at 6000 G in 4 ºC temperature for 10 minute. The centrifuged extract was used to analyze the maximum enzyme activity by heating the extract at 45–65 ºC range temperature and 5–20 minute range time. Maximum enzyme activity analysis obtained at 55 ºC for 5 minute for the sample duodenum, jejunum, ileum, colon respectively were 4, 3482 U/ml, 3,9247 U/ml, 3,9176 U/ml, and 3,0353 U/ml. Protease from extract enzyme has seven bands with molecular weight 66,54 kDa, 57,61 kDa, 48,94 kDa, 48,47 kDa, 36,80 kDa, 24,28 kDa, and 12,80 kDa. The enzyme has optimum temperature at 55 ºC and optimum at pH 9, and also inhibited by ion Ca2+ and Mg2+ . The in vitro analysis used chicken powder showed no keratinase activity.
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