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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Journal of the Indonesian Mathematical Society
Kuntjoro Adji Sidarto
Industrial and Financial Mathematics Research Group, Institut Teknologi Bandung, Indonesia
Mathematics

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Model of Deposit and Loan of A Bank Using Spiral Optimization Algorithm Ansori, Moch Fandi; Sidarto, Kuntjoro Adji; Sumarti, Novriana
Journal of the Indonesian Mathematical Society Volume 25 Number 3 (November 2019)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.25.3.826.292-301

Abstract

Nowadays, the study of financial stability of banking is important, which is to observe the behavior of the bank in the future. In this paper, a simple model of deposit and loan of a bank is solved analytically and numerically, and then it is implemented into data of four groups of commercial banks in Indonesia based on their capitals. From the data for each group of banks, the parameters will be estimated using the Spiral Optimization Algorithm. The results show that the algorithm gives satisfactory solutions in terms of closeness between the analytical and numerical solutions. In the long run, the deposit and loan volumes will be stable at their equilibrium points which showing the good condition of the future of the banks based on current state.
Pricing Modified Barrier Options Using the Bino-Trinomial Tree Model: A Strategy for Loss Minimization Rahayu, Rima Aulia; Agustina, Fitriani; Sidarto, Kuntjoro Adji
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.33239

Abstract

A particular exotic option that is widely traded in the global financial market is the barrier option. Barrier options are attractive because they have a limit that must be reached to activate the option. These limits may be utilized by investors as a point of reference to minimize potential losses. Accordingly, the researcher attempts to use the bino-trinomial tree model as a new approach to minimize losses. The purpose of this study is to analyze the bino-trinomial tree model to provide investors with more flexible hedging experience. The bino-trinomial tree model is obtained by combining the trinomial tree model at the first stage, then the binomial tree model at a further stage. This analysis was conducted by calculating the type of knock-out european call options. The results demonstrate that this model can effectively, accurately and flexibly manage the complex options required by modern investors, including multi-step single moving barrier options and single window barrier options.
CONSTRUCTION OF THE BINO-TRINOMIAL METHOD USING THE FUZZY SET APPROACH FOR OPTION PRICING Agustina, Fitriani; Sumarti, Novriana; Sidarto, Kuntjoro Adji
Journal of the Indonesian Mathematical Society Vol. 30 No. 2 (2024): JULY
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.2.1775.179-204

Abstract

An option is a financial instrument that investors often use for speculation or hedging purposes. Calculating the profit in the investment using options also considers its price, so the investor needs to know the proper value of the option's price or at least the range of these values. This paper aims to improve the Bino-Trinomial tree model for determining the price of a European call option with a volatility parameter in the form of a triangular Fuzzy number. The Bino-Trinomial tree model is a combination of the Binomial and Trinomial trees that aims to control the values of its branches. Due to the involvement of the Fuzzy number, the obtained value of the option price is in a range or interval, so the investor could use it appropriately in arranging investment strategies. In the proposed model, the Fuzzy volatility parameter is utilized to capture the uncertainty of the estimated volatility in the financial market which can fluctuate from time to time. This parameter is expected to provide reasonable ranges and appropriate Fuzzy membership functions for option pricing so that investors can expect different optimal values for different risk preferences. We also adjusted the formulation of the increase and decrease factors in the Fuzzy Binomial tree to model stock price movements. Using different values of the volatility's sensitivity level and the option period, the results of numerical simulations show that prices of European call options given by the market are always within the option price range of the proposed model's result. Likewise, the results of the defuzzification of options prices in our Fuzzy Bino-Trinomial tree model are not much different from the prices given by the market. This shows that the Fuzzy Bino-Trinomial tree model performs better in determining the price of European call options than the Fuzzy Binomial tree and Fuzzy Trinomial models.
Co-Authors Fitriani agustina Moch Fandi Ansori Novriana Sumarti Rahayu, Rima Aulia