Judul: Penentuan Harga Opsi Chooser dengan Menggunakan Metode Binomial.
Abstrak: Opsi chooser adalah opsi yang memberikan hak kepada pemilik opsi untuk memutuskan di beberapa titik dalam waktu sebelum jatuh tempo apakah menjadikan opsi tersebut sebagai opsi call atau opsi put. Karya ilmiah ini membahas tentang penentuan harga opsi chooser tipe Eropa menggunakan metode binomial dan menganalisis pengaruh beberapa parameter terhadap harga opsi chooser. Nilai hampiran opsi chooser dihitung menggunakan metode binomial, sedangkan nilai “eksak” didapatkan dari mengambil nilai hampiran dengan n (langkah) yang besar. Berdasarkan hasil penghitungan, pergerakan nilai opsi awalnya berfluktuasi kemudian nilai hampiran opsi chooser tipe Eropa semakin mendekati nilai “eksak” sehingga akan konvergen ke suatu nilai tertentu seiring bertambahnya langkah binomial.
Keyword: konvergen, metode binomial, opsi call, opsi chooser, opsi put

Judul: Penentuan harga opsi compound tipe eropa dengan model binomial
Abstrak: Opsi compound merupakan opsi dari suatu opsi lainnya. Nilai payoff opsi compound melibatkan nilai opsi vanilla sebagai underlying assets. Opsi compound tipe Eropa adalah opsi Eropa yang underlying asset-nya berupa opsi tipe Eropa. Opsi ini memiliki dua waktu eksekusi dan dua harga eksekusi. Karya ilmiah ini membahas tentang penentuan nilai opsi compound tipe Eropa menggunakan model binomial dan penentuan orde kekonvergenan metode numeriknya. Nilai hampiran opsi compound dihitung menggunakan model binomial, sedangkan nilai analitik dihitung menggunakan formula Black-Scholes. Berdasarkan hasil penghitungan, semakin banyak langkah yang digunakan pada model binomial, nilai hampiran opsi compound tipe Eropa semakin mendekati nilai analitik, sehingga dapat dinyatakan model binomial konvergen.
Keyword: exotic options, European compound options, binomial models, convergence order

Judul: Extracellular Expression of thermostable Geobacillus stearothermophilus T1.2RQ Lipase for Biodiesel Production
Abstrak: The extracellular expression of enzymes in an excellent secretion host such as Bacillus subtilis is a useful strategy for making enzymes of industrial significance more affordable by lowering the cost of its downstream processing. Lipases are a category of hydrolases that catalyze the hydrolysis of triglycerides to glycerol and free fatty acids. Also, lipases catalyze the hydrolysis and transesterification of other esters as well as the synthesis of esters. They can perform very specific biotransformation reactions and are widely used in food, organic synthesis, detergents, cosmetic, and pharmaceutical industries. Geobacillus stearothermophilus T1.2RQ lipase is an industrially-desired thermostable lipolytic enzyme with an excellent hydrolytic and transesterification activity. This study aimed to express T1.2RQ lipase, in B. subtilis WB800 and ensure its secretion into the extracellular medium. Three signal peptides (AmyQ, Epr, LipA) and two promoters (Pgrac01 and Pgrac100) were used in the secretory-expression of T1.2RQ lipase, based on five constructed expression vectors constructed by restriction cloning and PCR mutagenesis. Sangers sequencing was used to verify constructs to ensure they are in the correct reading frame. Recombinants vectors, pHT43 (plasmid control), pHT43-T1.2RQ, pHT43- T1.2RQ_AmyQ, pHT43-T1.2RQ_Epr, and pHT43-T1.2RQ_LipA, were transformed by electroporation into Bacillus subtilis WB800. The electroporation was successful with the optimum condition of 2500V, 200 ohms, 25µF, and 5milliseconds. Recombinant B. subtilis pHT43 (negative control) and pHT43-T1.2RQlip + signal peptides were streaked on the lipidic agar, LA+TBN. All four recombinants, including the negative control (B. subtilis WB800-pHT43), produced clear zones on the TBN agar plate after overnight incubation (fig 2), indicating the presence of a lipolytic enzyme in all of the recombinant B. subtilis cells. pHT43-T1.2RQlip + signal peptides (AmyQ, Epr, and LipA) have clear zones with significantly higher diameters than B. subtilis WB800-pHT43 (negative control). This phenomenon suggests that the recombinant thermostable lipase T1.2RQ introduced into these cells was successfully expressed, thereby increasing the lipolytic capability of its host cells T1.2RQ lipase was expressed in 50ml terrific broth medium (TB) and the expression induced with 1mM IPTG. Lipase activity assay using p-nitrophenyl esters showed that all three signal peptides directed the secretion of T1.2RQ lipase into the extracellular medium. Signal peptide, LipA, resulted in the highest extracellular activity of 5.6 U/mL, which corresponds to a 6-fold increase over the parent B. subtilis WB800 strain. Meanwhile, signal peptides, AmyQ and Epr produced 4.2 U/mL and 3.4 U/mL activity respectively. SDS-Zymogram analysis confirmed that T1.2RQ lipase was correctly processed and secreted in its original size of 44 kDa. An attempt to further increase lipase expression level by promoter optimization showed that, contrary to expectation, promoter Pgrac100 exhibited similar expression levels as the original Pgrac01. Nevertheless, the demonstration of the successful secretion of T1.2RQ lipase in this work confirms the latter as a promising approach for the industrial production of the enzyme
Keyword: Bacillus subtilis, Expression, Extracellular, Heterologous, Lipase, Thermostable