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All Journal Jurnal Matematika Buletin Udayana Mengabdi E-Jurnal Matematika Prosiding Seminar Nasional MIPA Jurnal Matematika Sains dan Teknologi BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) International Journal of Applied Mathematics and Computing.
Komang Dharmawan
Prodi Matematika FMIPA Universitas Udayana
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Transportation Other

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ESTIMASI CVAR PADA PORTOFOLIO SAHAM MENGGUNAKAN METODE GJR-EVT DENGAN PENDEKATAN D-VINE COPULA DERY MAULANA; KOMANG DHARMAWAN; I GUSTI AYU MADE SRINADI
E-Jurnal Matematika Vol 11 No 2 (2022)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2022.v11.i02.p372

Abstract

Risk measure using Conditional Value at Risk can be calculate if values that exceeds the p-quantile is known in VaR. The models used to accommodate characteristics of the stock portfolio in this research are EVT-GARCH-D-vine copula and EVT-GJR-D-vine copula so the performance of these two models can be compared. A comparison of the performance of the EVT-GARCH-D-vine copula and EVT-GJR-D-vine copula models can be seen from the Kupiec test backtesting process. Exceeded value Kupiec Test on CVaR 99% is 2, CVaR 95% is 6, and CVaR 90% is 13 for AR(1)-GARCH-t(1,1)-GPD and CVaR 99% is 3, CVaR 95% is 7, and CVaR 90% is 13 for AR(1)-GJR-t(1,1)-GPD. The Kupiec test describes the estimated risk value of CVaR running well with the value of the entire model above the significant level of ? = 0.05 so as to provide a conclusion of risk estimates considered feasible.
PENGGUNAAN SIMULASI MONTE CARLO DALAM ESTIMASI VALUE AT RISK (VaR) PORTOFOLIO YANG DIBENTUK DARI INDEKS HARGA SAHAM MULTINASIONAL NABILA NUR JANNAH; KOMANG DHARMAWAN; LUH PUTU IDA HARINI
E-Jurnal Matematika Vol 11 No 3 (2022)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2022.v11.i03.p381

Abstract

Investment is buying an asset that is expected in the future can be resold and get a high profit value. There are two factors that must be considered when you want to invest in stocks, namely the rate of return on stocks and risk factors. By forming a portfolio is expected to minimize a risk. Value at Risk (VaR) is a form of measurement of risk when making investments. In this study VaR will be calculated using the Monte Carlo Simulation method and the Historical method. This study aims to find out var portfolio estimates involving JCI and DJIA stock indices from two different countries as well as to find out the differences between VaR using Historical and VaR using Monte Carlo Simulations. From the stock index data obtained further determined the value of the parameters, namely the expected return and standard deviation values used to calculate the value of the VaR Portfolio, while the confidence increase used in this study was 99% and with a period of 1 or the next day. Based on the results of the VaR value study using the Monte Carlo Simulation method and the Historical method, the Historical method obtained results of 3,650,506 and 1,029,103. The results showed that VaR values using the Monte Carlo Simulation method got greater results than using the Historical method, because the Monte Carlo Simulation performed repeated iterations by including random number generators.
ESTIMASI VOLATILITAS STOKASTIK CRYPTOCURRENCY BITCOIN MENGGUNAKAN MODEL HESTON-MILSTEIN NI PUTU WIDYA ISWARI DEWI; KOMANG DHARMAWAN; I WAYAN SUMARJAYA
E-Jurnal Matematika Vol 11 No 4 (2022)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2022.v11.i04.p383

Abstract

Volatility is a quantity that measures how far a stock or cryptocurrency price moves in a certain period. To measure volatility properly, it can be done by using volatility modeling. The stochastic volatility model is one of the models used to predict volatility in a time series data, one of the stochastic volatility model is the Heston model. There are two schemes for estimating volatility using the Heston model, namely the Euler scheme and the Milstein scheme. The purpose of this study is to compare the estimation results of Bitcoin volatility with the two schemes. In using the Heston model, several parameters such as , , dan are needed. This parameter is calculated using the maximum likelihood estimation method. The results of the calculation of these parameters, respectively, are = 29.9996, =0.1464, and =2.1164. With the help of these three parameters, volatility estimation is generated. In this study, the Milstein scheme produces a lower volatility value than the Euler scheme.
PENENTUAN NILAI PREMI ASURANSI PERTANIAN BERBASIS HARGA INTERNASIONAL MENGGUNAKAN MODEL MEAN REVERSION DENGAN MUSIMAN I NYOMAN BRYAN ANDIKA; KOMANG DHARMAWAN; DESAK PUTU EKA NILAKUSMAWATI
E-Jurnal Matematika Vol 12 No 1 (2023)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2023.v12.i01.p401

Abstract

The seasonal cycle causes cocoa price movements in the international market to fluctuate. This certainly affects the development of cocoa prices at the producer level, causing uncertainty about the prices received by farmers. International price-based agricultural insurance is an alternative to protect farmers against global price fluctuations. Compensation is given if the global price of cocoa falls below the agreed trigger value. This study aims to calculate the fair premium value for agricultural insurance based on international prices for cocoa in the Tabanan Regency, Bali, which was simulated using a mean reversion model with seasonality. To perform the simulation, the first step is to estimate the parameters of the seasonal model and the mean reversion model. Next, simulate the international price of cocoa. Then, determine the trigger value based on the percentile of the simulation data. Finally, calculate the premium value using the cash-or-nothing put option with the Black-Scholes model. The results show that the premium value which is considered fair lies between 5,77% to 11,08% of the insured value.
PENERAPAN METODE SAFETY FIRST CRITERION PADA SELEKSI SAHAM UNTUK PEMBENTUKAN PORTOFOLIO OPTIMAL HAMITA HAKMI; KOMANG DHARMAWAN; RATNA SARI WIDIASTUTI
E-Jurnal Matematika Vol 12 No 2 (2023)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2023.v12.i02.p406

Abstract

The formation of an optimal portfolio can be done with the Safety First Criterion method which is based on down side risk, namely the risk of causing a loss. The purpose of this study is to determine the optimal portfolio using Safety First Criterion method. Safety first criteria for portfolio selection are concerned only with the risk of failing to achieve a criteria minimum target return or secure prespecified safety margins. There are three criteria for the Safety First, namely Roy, Kataoka and Telser criteria. The results of this study formed an optimal portfolio with different risk values the Roy criteria is 0.0486, Kataoka is 0.0487 and Telser is 0.0527. So that the best portfolio of the three criteria is Roy's criterion because it has the lowest risk value with expected return the same.
ESTIMASI EXPECTED SHORTFALL DALAM OPTIMALISASI PORTOFOLIO DENGAN METODE DOWNSIDE DEVIATION PADA SAHAM IDXHEALTH IDA BAGUS ANGGA DARMAYUDA; KOMANG DHARMAWAN; KARTIKA SARI
E-Jurnal Matematika Vol 12 No 2 (2023)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2023.v12.i02.p408

Abstract

Portfolio optimization using downside deviation is an optimal portfolio by defining the standard deviation of returns below the target (benchmark) as a level of risk measure. Every optimal portfolio certainly has risks. Therefore, it’s necessary to estimate the risk as an illustration of the worst investment condition. Expected shortfall is a measure of risk because it fulfills the coherent risk measures, and its estimated value exceeds VaR. This study aims to obtain optimal portfolio results using the downside deviation method and estimate portfolio risk using the expected shortfall model. The data used in this study are five stocks with the highest average trading volume that are incorporated into IDXHEALTH, namely SAME.JK, KLBF.JK, MIKA.JK, SIDO.JK, and IRRA.JK during the study period from 1 January 2020 to 23 September 2022. As a result obtained from this study, the combined weight of each stock in the optimal portfolio formed is, 2,8% in SAME.JK, 55,63% in KLBF.JK, 26,56% in MIKA.JK, 0,21% in SIDO.JK, and 14.8 % on IRRA.JK with a portfolio return of 0.0249%. The expected shortfall estimation value obtained accurately at a 99% confidence interval of 0.0399, whose value exceeds VaR (0.0343).
PENGELOMPOKAN SAHAM MENGGUNAKAN K-MEANS DALAM PEMBENTUKAN PORTOFOLIO OPTIMAL ADE AYU NITA DEVI; KOMANG DHARMAWAN; NI KETUT TARI TASTRAWATI
E-Jurnal Matematika Vol 12 No 4 (2023)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2023.v12.i04.p433

Abstract

K-Means clustering analysis is a technique used in grouping objects that have similar characteristics. In forming a portfolio, investors need a group of stocks from different sectors that aim to build a well-diversified portfolio. Portfolio diversification is the placement of assets from various stocks in such a way that risks can be minimized. This study aims to obtain the results of grouping stocks with K-Means at IDX80 and then determine the optimal portfolio of each cluster formed using the Mean Variance method in the period January, 1st 2020 to November, 10th 2022. As a result, obtained in this study that grouping with K -Means produces four groups and is the best portfolio consisting of 10 stocks with a Sharp ratio performance value of 0.0062 with a risk portfolio of 1.59% and an expected return portfolio of 0.17%.
ANALISIS RISIKO PORTOFOLIO KREDIT OBLIGASI KORPORASI MENGGUNAKAN METODE CREDITMETRICS I GUSTI MADE AYU ANGGUN TIARA PRATINI; KOMANG DHARMAWAN; NI KETUT TARI TASTRAWATI
E-Jurnal Matematika Vol 13 No 2 (2024)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2024.v13.i02.p452

Abstract

Bond is a medium or long-term debt agreement which when the bond matures will be paid back with the interest. Bonds are issued to obtain new fund flows to meet operational needs and strengthen financial position. One of the risks of bonds is credit risk. This risk occurs due to the issuer's inability to continue and complete its obligations. This risk often occurs in corporate bonds. So, investors need to conduct risk analysis and proper risk management. One method of credit risk analysis is the creditmetrics. In this method, credit score changes are not only caused by the probability of default, but also caused by migration of company ratings. This study aims to calculate the portfolio risk of six corporate bonds and determine the weight that must be given to each bond, so that the minimum risk will be obtained. The estimated portfolio risk obtained is Rp. 15.615 billion with an average portfolio value is Rp. 18.74 billion. Then the weight that must be given to each bond is the first bond of -1.308%, the second bond is -8.542%, the third bond is 32.798%, the fourth bond is 77.716%, the fifth bond is -1.982%, and the sixth bond is 1.317%.
ANALISIS PORTOFOLIO OPTIMAL PADA INVESTASI LOGAM MULIA EMAS MENGGUNAKAN METODE MEAN ABSOLUTE DEVIATION (MAD) DENGAN ESTIMASI PARAMETER GARCH(1,1) FEBBY VERENNIKA; KOMANG DHARMAWAN; LUH PUTU IDA HARINI
E-Jurnal Matematika Vol 13 No 2 (2024)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2024.v13.i02.p454

Abstract

This study aims to analyze the optimal portfolio in gold precious metal investments using the Mean Absolute Deviation (MAD) method combined with the GARCH(1,1) parameter estimation. The MAD method was chosen for its ability to measure portfolio risk more stably and simply compared to other methods like Mean-Variance. Meanwhile, the GARCH(1,1) model is used to estimate the volatility of gold prices, which are often influenced by global economic and geopolitical uncertainties. The data used in this study include daily stock prices of gold companies from January 2017 to June 2021. The analysis results show that the combination of the MAD method and GARCH(1,1) can provide a more comprehensive view of forming an optimal portfolio that maximizes returns and minimizes risks for gold investors. Based on the calculations, the optimal portfolio with the best performance was identified using the Sharpe, Treynor, and Jensen indices, which indicate the superiority of the first portfolio in terms of return and risk.
Estimasi Risiko Kredit Obligasi Dengan Suku Bunga Stokastik Berdasarkan Probability Of Default Surma, Odilia Gratiaplena; Dharmawan, Komang; Ida Harini, Luh Putu
Jurnal Matematika Vol 13 No 2 (2023)
Publisher : Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/JMAT.2023.v13.i02.p166

Abstract

Bonds as a fairly safe short-term and long-term investment product certainly still have potential investment risks. One of the risks in bond products is credit risk in the form of default, where the issuer fails to pay obligations to investors. The Merton model is one method that can be applied in estimating credit risk on bonds. The interest rate applied in the Merton model is generally a constant interest rate so that in this study the constant interest rate will be replaced by the stochastic interest rate of the Cross Ingersoll Ross (CIR) model. This study aims to calculate the probability of default by applying the CIR model interest rate in the Merton model of BRI bank based on a bond value of 605 billion and a bond contract period of 7 years. The results of the calculation of the CIR model interest rate of 7.28% by substituting it into the Merton model calculation obtained a probability of default value of 0.0% which indicates that there is no risk of default by BRI bank at maturity
Co-Authors A.A DWI MARSITA ANGGRAENI AA Sudharmawan, AA ADE AYU NITA DEVI AULIA ATIKA PRAWIBTA SUHARTO DERY MAULANA DESAK PUTU DEVI DAMIYANTI Desak Putu Eka Nilakusmawati DEVI NANDITA. N DEWA AYU AGUNG PUTRI RATNASARI ELVINA LIADI FEBBY VERENNIKA Fransisca Emmanuella Aryossi G. K Gandhiadi G. K. GANDHIADI Gandhiadi, G K GEDE SUMENDRA HAMITA HAKMI HERLINA HIDAYATI I G. A. Widagda I GEDE ARYA DUTA PRATAMA I GEDE ERY NISCAHYANA I GEDE RENDIAWAN ADI BRATHA I Gusti Ayu Made Srinadi I GUSTI AYU MITA ERMIA SARI I GUSTI MADE AYU ANGGUN TIARA PRATINI I GUSTI PUTU NGURAH MAHAYOGA I KOMANG GDE SUKARSA I KOMANG TRY BAYU MAHENDRA I NYOMAN BRYAN ANDIKA I Nyoman Widana I Putu Eka Nila Kencana I PUTU OKA PARAMARTHA I PUTU YUDHI PRATAMA I Wayan Sumarjaya I WAYAN WIDHI DIRGANTARA ICHA WINDA DIAN SAFIRA IDA AYU EGA RAHAYUNI IDA AYU GDE KHASMANA PUTRI IDA AYU PUTU CANDRA DEWI IDA BAGUS ANGGA DARMAYUDA IKHSAN AKBAR INTAN AWYA WAHARIKA INTAN LESTARI IRENE MAYLINDA PANGARIBUAN KADEK FRISCA AYU DEVI KADEK INTAN SARI KADEK MIRA PITRIYANTI Kartika Sari Ketut Jayanegara LUH HENA TERECIA WISMAWAN PUTRI LUH PUTU IDA HARINI Luh Putu Ratna Sundari LUSIA EMITRIANA MAGOL MADE ASIH MAKBUL MUFLIHUNALLAH MERARY SIANIPAR MIRANDA NOVI MARA DEWI N. N. Rupiasi NABILA NUR JANNAH NI KADEK NITA SILVANA SUYASA NI KADEK PUSPITAYANTI Ni Ketut Tari Tastrawati NI LUH NIKASARI NI LUH PUTU KARTIKA WATI Ni Luh Putu Suciptawati Ni Made Asih NI MADE NITA ASTUTI NI NYOMAN AYU ARTANADI Ni Nyoman Rupiasih NI PUTU AYUNDA SURYA DEWI Ni Putu Leony Putri Paramita NI PUTU WIDYA ISWARI DEWI NI WAYAN UCHI YUSHI ARI SUDINA PUTU AMANDA SETIAWANI PUTU AYU DENI PUTU IKA OKTIYARI LAKSMI PUTU MIRAH PURNAMA D. PUTU SAVITRI DEVI PUTU WIDYA ASTUTI Ratna Sari Widiastuti RISKA YUNITA SAYID QOSIM SORAYA SARAH AFIFAH Surma, Odilia Gratiaplena Susanti Marito Barus Swastika, Putu Veri Tjokorda Bagus Oka VIAN RISKA AYUNING TYAS VIKY AMELIAH WAYAN ARTHINI Wijayakusuma, I Gusti Ngurah Lanang WIRYA SEDANA Yan Ramona YOHANA Th.V. SERAN YOSEVA AGUNG PRIHANDINI