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All Journal Jurnal Matematika Buletin Udayana Mengabdi E-Jurnal Matematika Prosiding Seminar Nasional MIPA BIOTROPIA - The Southeast Asian Journal of Tropical Biology 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 Biochemistry, Genetics & Molecular Biology Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Energy Engineering Immunology & microbiology Mathematics Mechanical Engineering Physics Transportation Veterinary Other

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PERHITUNGAN VALUE AT RISK DENGAN PENDUGA VOLATILITAS STOKASTIK HESTON DESAK PUTU DEVI DAMIYANTI; KOMANG DHARMAWAN; LUH PUTU IDA HARINI
E-Jurnal Matematika Vol 7 No 4 (2018)
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.2018.v07.i04.p220

Abstract

Value at risk is a method that measures financial risk of an security or portfolio. The aims of the research is to find out the value at risk of an exchange rate using the Heston stochastic volatility model. Heston model is a strochastic volatility model that assumes that volatility of the security follow stochastic process and consider the mean reversion. Based on simulation results, the value of volatility using Heston volatility estimastor is 0.2887, and the value of Heston VaR with 95 percent confident level is 0.0297. Based on result of backtesting, there are 48 violations obtained VaR using Heston model, while historical VaR there are 2 violations. Thus, VaR using Heston model is more strict in estimating risk.
PERBANDINGAN CAPITAL ASSET PRICING MODEL (CAPM) DAN THREE FACTORS MODEL FAMA AND FRENCH (TFMFF) DALAM MENGESTIMASI RETURN SAHAM KADEK MIRA PITRIYANTI; KOMANG DHARMAWAN; G.K. GANDHIADI
E-Jurnal Matematika Vol 4 No 4 (2015)
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.2015.v04.i04.p109

Abstract

In 1996, Fama and French developed the CAPM in Three Factor Model Fama and French (TFMFF) to analyze the relationship between risk with rate of return by adding firm size factor that is proxied by Small Minus Big (SMB) and value factor at Book to Market Ratio that is proxied by High Minus Low (HML) on the CAPM model. The aim of this research is to compare the ability of CAPM and TFMFF in estimating the returns on six types of portfolios which are formed based on firm size and BE/ME. Selected samples are stocks of LQ-45 in period of February 2014, which have passed the selection of firm profits and ROE Warren Buffett criteria. Simple linear regression and Multiple linear regression with t test and F test statistics are used to demonstrate the influence and significance level of each variable. The results showed that TFMFF was more superior than CAPM. Market risk factor consistently affected each portfolio. SMB and HML is not always significantly effect on each portfolio, such as portfolio B/H, only market risk factor has a significant effect. However, the addition of SMB factors and HML factors could increase the coefficient of determination in each formed portfolio.
IMPLEMENTASI METODE MARKOV CHAIN MONTE CARLO DALAM PENENTUAN HARGA KONTRAK BERJANGKA KOMODITAS PUTU AMANDA SETIAWANI; KOMANG DHARMAWAN; I WAYAN SUMARJAYA
E-Jurnal Matematika Vol 4 No 3 (2015)
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.2015.v04.i03.p099

Abstract

The aim of the research is to implement Markov Chain Monte Carlo (MCMC) simulation method to price the futures contract of cocoa commodities. The result shows that MCMC is more flexible than Standard Monte Carlo (SMC) simulation method because MCMC method uses hit-and-run sampler algorithm to generate proposal movements that are subsequently accepted or rejected with a probability that depends on the distribution of the target that we want to be achieved. This research shows that MCMC method is suitable to be used to simulate the model of cocoa commodity price movement. The result of this research is a simulation of future contract prices for the next three months and future contract prices that must be paid at the time the contract expires. Pricing future contract by using MCMC method will produce the cheaper contract price if it compares to Standard Monte Carlo simulation.
MODEL NON LINIER GARCH (NGARCH) UNTUK MENGESTIMASI NILAI VALUE at RISK (VaR) PADA IHSG I KOMANG TRY BAYU MAHENDRA; KOMANG DHARMAWAN; NI KETUT TARI TASTRAWATI
E-Jurnal Matematika Vol 4 No 2 (2015)
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.2015.v04.i02.p090

Abstract

In investment, risk measurement is important. One of risk measure is Value at Risk (VaR). There are many methods that can be used to estimate risk based on VaR framework. One of them Non Linier GARCH (NGARCH) model. In this research, determination of VaR used NGARCH model. NGARCH model allowed for asymetric behaviour in the volatility such that “good news” or positive return and “bad news” or negative return. Based on calculations of VaR, the higher of the confidence level and the longer the investment period, the risk was greater. Determination of VaR using NGARCH model was less than GARCH model.
PENERAPAN STATIC HEDGE DALAM PENGELOLAAN RISIKO PADA OPSI TIPE BARRIER NI MADE NITA ASTUTI; KOMANG DHARMAWAN; TJOKORDA BAGUS OKA
E-Jurnal Matematika Vol 7 No 4 (2018)
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.2018.v07.i04.p225

Abstract

The barrier option is an option whose payoff depends on whether the underlying asset touches the barrier or not during the lifetime of the option. The determination of the barrier option requires a numerical approach, one of which is the Binomial Tree model. The purpose of this study is to determine barrier option type down and out call on a static hedging using the Binomial Tree model and compare it with the analytic value. The results show that the increases in strike price would decrease the option value. Moreover, values from 80 periods using the Binomial Tree model for the four strike prices are close to analytic with error less than or equal to 0.00182.
PENENTUAN NILAI KONTRAK OPSI SAHAM TIPE EROPA MENGGUNAKAN MODEL CONSTANT ELASTICITY OF VARIANCE LUSIA EMITRIANA MAGOL; KOMANG DHARMAWAN; DESAK PUTU EKA NILAKUSMAWATI
E-Jurnal Matematika Vol 9 No 1 (2020)
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.2020.v09.i01.p276

Abstract

Investment is a very sensitive matter especially relating to securities commonly known as shares. Shares are not merely as securities or certificates of ownership but as a business area in achieving profits. One alternative factor for investment is option. Stock options are one of the trading tools used to secure stock investments owned by investors. The real value of stock options can be known when the due date. The stock option value formula can be used to find out the value before the due date. The most widely known stock option value is to use the Black-Scholes equation which is obtained from a constant volatility value. Then it was developed because it saw the conditions in the market based on the volatility of the value (not constant). The purpose of this study is to determine the value of stock options in the market based on volatile values ??that change using the Constant Elasticity of Variance model with the limit of European stock purchase options. If the resulting stock option value is greater than the option price in the market, investors are advised to buy the stock option.
PENENTUAN HARGA OPSI BELI TIPE ASIA DENGAN METODE MONTE CARLO-CONTROL VARIATE NI NYOMAN AYU ARTANADI; KOMANG DHARMAWAN; KETUT JAYANEGARA
E-Jurnal Matematika Vol 6 No 1 (2017)
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.2017.v06.i01.p145

Abstract

Option is a contract between the writer and the holder which entitles the holder to buy or sell an underlying asset at the maturity date for a specified price known as an exercise price. Asian option is a type of financial derivatives which the payoff taking the average value over the time series of the asset price. The aim of the study is to present the Monte Carlo-Control Variate as an extension of Standard Monte Carlo applied on the calculation of the Asian option price. Standard Monte Carlo simulations 10.000.000 generate standard error 0.06 and the option price convergent at Rp.160.00 while Monte Carlo-Control Variate simulations 100.000 generate standard error 0.01 and the option price convergent at Rp.152.00. This shows the Monte Carlo-Control Variate achieve faster option price toward convergent of the Monte Carlo Standar.
PENENTUAN HARGA KONTRAK OPSI TIPE EROPA MENGGUNAKAN METODE QUASI MONTE CARLO DENGAN BARISAN KUASI-ACAK HALTON I GUSTI PUTU NGURAH MAHAYOGA; KOMANG DHARMAWAN; LUH PUTU IDA HARINI
E-Jurnal Matematika Vol 3 No 4 (2014)
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.2014.v03.i04.p078

Abstract

Penelitian ini bertujuan untuk mengetahui keakuratan hasil simulasi harga saham untuk menentukan harga opsi call dari metode Monte Carlo dan metode Quasi Monte Carlo dengan menggunakan program Matlab. Harga standar yang digunakan untuk membandingkan kedua metode tersebut akan dihitung dengan metode Black-Scholes. Nilai error yang dihitung menggunakan metode MAPE (Mean Absolute Percentage Error) digunakan sebagai acuan dalam perbandingan. Selain keakuratan simulasi harga saham, kecepatan eksekusi program Matlab kedua metode juga dihitung untuk efisiensi waktu. Tahap pertama, menentukan variabel-variabel yang digunakan untuk menghitung lintasan harga saham pada waktu ke-t pada saat mensimulasikan harga saham. Tahap kedua, menghitung harga standar menggunakan metode Black-Scholes. Tahap ketiga, mensimulasikan harga saham dengan metode Monte Carlo dan Quasi Monte Carlo. Setelah mensimulasikan harga saham, catat waktu eksekusi program Matlab, lalu dihitung nilai pay-off dari opsi call, kemudian menaksir harga opsi call dengan merata-ratakan seluruh nilai pay-off dari masing-masing iterasi. Tahap terakhir, menghitung error dari kedua metode simulasi dengan metode MAPE lalu membandingkannya. Hasil penelitian ini menunjukkan bahwa metode Quasi Monte Carlo lebih akurat karena menghasilkan nilai error yang lebih kecil, artinya hasil simulasinya mendekati harga standar. Sedangkan untuk waktu eksekusi program, metode Monte Carlo lebih baik di semua iterasi.
PERHITUNGAN VaR PORTOFOLIO SAHAM MENGGUNAKAN DATA HISTORIS DAN DATA SIMULASI MONTE CARLO WAYAN ARTHINI; KOMANG DHARMAWAN; LUH PUTU IDA HARINI
E-Jurnal Matematika Volume 1, No 1, Tahun 2012
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.2012.v01.i01.p001

Abstract

Value at Risk (VaR) is the maximum potential loss on a portfolio based on the probability at a certain time.  In this research, portfolio VaR values calculated from historical data and Monte Carlo simulation data. Historical data is processed so as to obtain stock returns, variance, correlation coefficient, and variance-covariance matrix, then the method of Markowitz sought proportion of each stock fund, and portfolio risk and return portfolio. The data was then simulated by Monte Carlo simulation, Exact Monte Carlo Simulation and Expected Monte Carlo Simulation. Exact Monte Carlo simulation have same returns and standard deviation  with historical data, while the Expected Monte Carlo Simulation satistic calculation similar to historical data. The results of this research is the portfolio VaR  with time horizon T=1, T=10, T=22 and the confidence level of 95 %, values obtained VaR between historical data and Monte Carlo simulation data with the method exact and expected. Value of VaR from both Monte Carlo simulation is greater than VaR historical data.
PERHITUNGAN VALUE AT RISK KUNJUNGAN WISATAWAN ASING KE BALI AGUS PUTU SURYAWAN; KOMANG DHARMAWAN; I GUSTI AYU MADE SRINADI
E-Jurnal Matematika Vol 9 No 1 (2020)
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.2020.v09.i01.p281

Abstract

The development of the tourism industry in Bali is very fast compared to other regions in Indonesia. This is due to the fascination of Bali which fascinates tourists, such as culture, customs and natural beauty. The rapid development of tourism in Bali requires tourism risk management. The purpose of this study is to calculate the Value At Risk (VaR) of Chinese, British and American tourists visiting Bali. The study was conducted using the VaR method with the GARCH (1,1) and GJR (1,1) models. Chinese tourist visit data is homocedasticity so it cannot proceed to GARCH (1.1) and GJR (1.1) modeling. VaR value of British and American tourist visits using the GARCH (1.1) and GJR (1.1) models at 95% confidence levels respectively -69.2% and -43.6 with an average VaR value of -56, 4%, and -69.3% and -44.7% with an average VaR of -57%. This means that if the Bali Government targets the number of tourist visits to be 7,100,000 people with a tourism promotion cost of Rp.134.1 per person, then there will be at least 4,004,400 people visiting Bali. So the investment costs incurred by the Provincial Government of Bali for tourism promotion of Rp. 536,990,040.
Co-Authors A.A DWI MARSITA ANGGRAENI AA Sudharmawan, AA ADE AYU NITA DEVI AULIA ATIKA PRAWIBTA SUHARTO Batho, Yanuarius Felix 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 Ida Bagus Gede Darmayasa IKHSAN AKBAR Inabuy, Fainmarinat selviani 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 Eka Sudaryatma 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 Teriyani, Ni Made 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