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: Numerical solution of the black-scholes model using upwind finite difference methods
Abstrak: Produk derivatif adalah instrumen keuangan yang nilainya bergantung pada nilai aset. Salah satu produk derivatif yang diperdagangkan dalam pasar keuangan adalah opsi. Opsi merupakan suatu kontrak antara dua pihak, yaitu pembeli dan penjual yang memberikan hak untuk membeli atau menjual suatu aset tertentu dengan harga dan waktu yang ditentukan. Berdasarkan waktu eksekusinya, opsi dibagi menjadi opsi tipe Eropa dan opsi tipe Amerika. Model yang digunakan untuk menentukan harga opsi tipe Eropa adalah model Black-Scholes yang merupakan persamaan diferensial parsial dengan nilai awal dan syarat batasnya bergantung pada jenis opsinya. Model ini dapat diselesaikan secara numerik dengan menggunakan metode beda hingga. Pada karya ilmiah ini, metode yang akan digunakan adalah metode implisit pada diskretisasi waktu dan metode beda hingga upwind pada diskretisasi ruang. Contoh numerik juga diberikan untuk menunjukkan kekonvergenan metode ini. Kata kunci: metode beda hingga, model Black-Scholes, opsi, Derivative product is a financial instrument in which the value was based on certain asset value which is called the underlying asset. One of derivative products traded in the financial market is called option, which is a contract between two parties, the buyer and the seller, in which the parties give a right to buy or sell the underlying asset by a certain price within a certain time frame. Based on the execution time, the time options are divided into two types, the European option and the American option. Models that are used to determine the European option price is called Black-Scholes model. The model is in the form of a partial differential equation with initial and boundary conditions depend on the type of options either call option or put option. This model can be solved numerically using the finite difference method. In this paper, we use implicit method for time stepping and an upwind finite difference method for spatial discretization. Numerical examples are also provided to show the convergence of this method. Key words: Black-Scholes model, finite difference method, option
Keyword: metode beda hingga, model Black-Scholes, opsi

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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