Judul: Penentuan Nilai Opsi Tipe Eropa dan Amerika Menggunakan Metode Binomial
Abstrak: Investors have purposes to obtain maximum returns, but they must be careful to invest their money because they may take risk. Therefore, they need products to reduce the risk. The products are called derivative products. There are many kinds of derivative products, such as options. An option is a type of contract between two parties. One party gives the other party a right to sell or to buy some assets in a certain price and in a certain period. Based on their execution time, there are two types of options i.e. European styles and American styles. European style options can only be exercised at expiration time, meanwhile American style options can be exercised at random time to the expiration time. In this paper, the option price at a discrete time will be determined by using binomial model. A binomial model is a model that describes asset price movements by assuming two possibilities of asset price movements in the future. Those are up and down. One-step binomial structures can be expanded into multistep binomial structures in order to approximate the option price. The application of one-step binomial model is used on the European option and multi-step binomial model is used on the American option. The acquired formula is applied to calculate the value of call option of PT Telekomunikasi Indonesia stocks in January 2012 based on the data of January to December 2011’s fluctuation of stock.
Keyword: American Style., European Style, Options, Binomial Model

Judul: Pemodelan Nilai Opsi Tipe Eropa
Abstrak: Option is the right to sell or buy a specified quantity of some underlying asset by paying a specified exercise price, on or before an expiration date. There are two basic types of options, calls and puts. A call option is the right to buy and a put option is the right to sell the underlying asset. There are two types of options according to its execution time, i.e. American and European options. American options can be exercised at any time the holder wishes until the expiration date, while European options can only be exercised on the expiration date. Modelling of option price usually is done analytically by determining solution of differential equation that is satisfied by the price of derivative asset, known as Black-Scholes equation. Because option price is a reflection of present value of expectation of difference between the exercise price and the stock price at expiration date, so it is necessary to study the option price through the concept of present value, as an alternative way to model the option price. The result of this study shows that modelling of option price using differential equation method and present value approach give the same option price. Furthermore the results of ilustration give informations about the relation of the option price with its parameters as follow: First, increase in the current stock price causes the call option price also to increase, while the put option price, on the contrary, will decrease. Second, increase in the exercise price causes the call option price to decrease, while the put option price will increase. Third, the longer the expiration time the call option price will be higher, while the put option price doesn’t have the same tendency, but it depends on other parameters. Fourth, increase in the interest rate causes the call option price to increase, while the put option price will decrease. Finally, increase in the volatility causes the price of both call option and put option will increase.
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Judul: The Dynamics of Water Chemical Properties in Acid Sulfate Area
Abstrak: Pada Oktober 2015 dan November 2019, air Sungai Segah di Kabupaten Berau secara spektakuler menjadi jernih ketika sebelumnya tampak berwarna coklat dan keruh. Selain airnya yang jernih, beberapa flok hasil proses flokulasi juga terlihat mengambang di beberapa bagian sungai. Hasil investigasi awal di sepanjang Sungai Segah, menunjukkan bahwa fenomena air jernih ini bermula dari perkebunan kelapa sawit milik Perusahaan A dan B. Sejak itu, media massa setempat gencar menyebarkan informasi tentang kegiatan pemupukan atau tumpahan pupuk di sungai tersebut oleh perkebunan kelapa sawit yang menyebabkan air jernih di sepanjang Sungai Segah. Pernyataan media massa lokal itu tampaknya dipertanyakan, karena harga pupuk yang mahal dan debit air di Sungai Segah tinggi. Penyebab terjadinya fenomena air jernih di Sungai Segah adalah adanya air asam yang banyak mengandung aluminium terlarut (273 ppm), hasil dari proses oksidasi pirit pada tanah sulfat masam di area perkebunan kelapa sawit. Selama musim kemarau yang panjang, pirit di tanah sulfat masam teroksidasi, dan ketika hujan deras, air asam yang mengalir ke sungai menyebabkan ikatan di antara partikel-partikel lumpur dan mengakibatkan air sungai menjadi jernih. Diperlukan beberapa upaya untuk meningkatkan pH air asam seperti penambahan zat basa dan pembilasan rutin dengan membuka pintu air perkebunan secara berkala yang akan mengalirkan air tidak asam dari perkebunan ke sungai. Penelitian ini bertujuan untuk mengetahui apakah upaya-upaya yang dilakukan dapat menurunkan aluminium terlarut dalam air asam, guna mencegah terjadinya flokulasi yang menyebabkan penjernihan air di Sungai Segah. Beberapa sampel air dari air parit perkebunan dianalisis kadar aluminium terlarut dan pH-nya pada tiga waktu yang berbeda, yaitu pada bulan Agustus 2020, Januari 2021, dan Agustus 2021. Hasil penelitian menunjukkan kecenderungan penurunan kadar aluminium terlarut diikuti dengan peningkatan pH. Kandungan aluminium terlarut tertinggi adalah 19,08 ppm, dan pH air mendekati netral pada pengukuran akhir. Dengan demikian, dapat disimpulkan bahwa upaya perbaikan dapat mengurangi kandungan aluminium terlarut dalam air untuk mencegah terjadinya penjernihan air di Sungai Segah., In October 2015 and November 2019, the water of Segah River in Berau Regency spectacularly became clear when it was appeared brown and muddy before. Besides clear water, some flocs which was the result of flocculation process were spotted floating in some part of the river. The initial investigation result along the Segah River, showed that the clear water phenomenon was started from the palm oil plantation owned by Company A and Company B. Since then, the local mass media aggressively shared the information about fertilization activity or spilled fertilizer on the river by an oil palm plantation caused clear water along Segah River. The statement of those local mass media seems questionable, since fertilizer was costly and the flow rate of water in Segah River is high. The cause of clear water phenomenon in Segah River was the acidic water that contained large amount of soluble aluminum (273 ppm), a result of pyrite oxidation process on acid sulfate soil in the oil palm plantation area. During a long dry season, pyrite in the acid sulfate soil was oxidized, and when the heavy rainfall came, acidic water flowed to the river caused bonding among the particles of the mud and
Keyword: air jernih, aluminium, pH, pirit, Sungai Segah