scholarly journals MENENTUKAN PORTOFOLIO OPTIMAL PADA PASAR SAHAM YANG BERGERAK DENGAN MODEL GERAK BROWN GEOMETRI MULTIDIMENSI

2015 ◽  
Vol 4 (3) ◽  
pp. 127 ◽  
Author(s):  
RISKA YUNITA ◽  
KOMANG DHARMAWAN ◽  
LUH PUTU IDA HARINI
Keyword(s):  
Stochastic Process ◽  
Exact Solution ◽  
Brownian Motion ◽  
Stock Price ◽  
Stock Return ◽  
Geometric Brownian Motion ◽  
Optimal Portfolio ◽  
The Future ◽  
Model Determination ◽  
Stock Price Movements

Model of stock price movements that follow stochastic process can be formulated in Stochastic Diferential Equation (SDE). The exact solution of SDE model is called Geometric Brownian Motion (GBM) model. Determination the optimal portfolio of three asset that follows Multidimensional GBM model is to be carried out in this research.Multidimensional GBM model represents stock price in the future is affected by three parameter, there are expectation of stock return, risk stock, and correlation between stock return. Therefore, theory of portfolio Markowitz is used on formation of optimal portfolio. Portfolio Markowitz formulates three of same parameter that is calculated on Multidimensional GBM model. The result of this research are optimal portfolio reaches with the proportion of fund are 39,38% for stock BBCA, 59,82% for stock ICBP, and 0,80% for stock INTP. This proportion of fund represents value of parameters that is calculated on modelling stock price.

scholarly journals PERSAMAAN DIFERENSIAL ORNSTEIN-UHLENBECK DALAM PERAMALAN HARGA SAHAM

2020 ◽  
Vol 13 (1) ◽  
pp. 60-67
Author(s):  
Amam Taufiq Hidayat ◽  
Subanar Subanar
Keyword(s):  
Brownian Motion ◽  
Stock Price ◽  
Stock Return ◽  
Compound Poisson Process ◽  
Geometric Brownian Motion ◽  
Data Simulation ◽  
Uhlenbeck Process ◽  
Stock Return Volatility ◽  
Ornstein Uhlenbeck Process ◽  
Brown Motion

Geometric Brownian motion is one of the most widely used stock price model. One of the assumptions that is filled with stock return volatility is constant. Gamma Ornstein-Uhlenbeck process a model to describe volatility in finance. Additionally, Gamma Ornstein-Uhlenbeck process driven by Background Driving Levy Process (BDLP) compound Poisson process and the marginal law of volatility follows a Gamma distribution. Barndorff-Nielsen and Shepard (BNS) Gamma Ornstein-Uhlenbeck model can to sample the process for the stock price with volatility follows Gamma Ornstein-Uhlenbeck process. Based on these, the simulation result are compared BNS Gamma Ornstein-Uhlenbeck model with geometric Brown motion for Standard and Poor (SP) 500 stock data. Simulation result give BNS Gamma Ornstein-Uhlenbeck model and Geometric Brownian motion a Root Mean Square Error (RMSE) are 0,13 and 0,24 respectively. These result indicate that the BNS Gamma  Ornstein-Uhlenbeck model gives a more accurate  than Geometric Brownian motion

scholarly journals The Geometric Brownian Motion of Indosat Telecommunications Daily Stock Price During the Covid-19 Pandemic in Indonesia

2021 ◽  
Vol 2084 (1) ◽  
pp. 012012
Author(s):  
Tiara Shofi Edriani ◽  
Udjianna Sekteria Pasaribu ◽  
Yuli Sri Afrianti ◽  
Ni Nyoman Wahyu Astute
Keyword(s):  
Brownian Motion ◽  
Stock Price ◽  
Service Providers ◽  
Main Idea ◽  
Geometric Brownian Motion ◽  
Government Policies ◽  
Percentage Error ◽  
Price Movement ◽  
Data Movement ◽  
Total Data

Abstract One of the major telecommunication and network service providers in Indonesia is PT Indosat Tbk. During the coronavirus (COVID-19) pandemic, the daily stock price of that company was influenced by government policies. This study addresses stock data movement from February 5, 2020 to February 5, 2021, resulted in 243 data, using the Geometric Brownian motion (GBM). The stochastic process realization of this stock price fluctuates and increases exponentially, especially in the 40 latest data. Because of this situation, the realization is transformed into log 10 and calculated its return. As a result, weak stationary in variance is obtained. Furthermore, only data from December 7, 2020 to February 5, 2021 fulfill the GBM assumption of stock price return, as R t 1 * , t 1 * = 1 , 2 , 3 , … , 40 . The main idea of this study is adding datum one by one as much as 10% – 15% of the total data R t 1 * , starting from December 4, 2020 backwards. Following this procedure, and based on the 3% < p-value < 10%, the study shows that its datum can be included in R t 1 * , so t 1 * = − 4. − 3 , − 2 , … , 40 and form five other data groups, R t 2 * , … , R t 6 * . Considering Mean Absolute Percentage Error (MAPE) and amount of data from each group, R t 6 * is selected for modelling. Thus, GBM succeeded in representing the stock price movement of the second most popular Indonesian telecommunication company during COVID-19 pandemic.

scholarly journals The application of model predictive control on stock portfolio optimization with prediction based on Geometric Brownian Motion-Kalman Filter

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Wawan Hafid Syaifudin ◽  
Endah R. M. Putri
Keyword(s):  
Brownian Motion ◽  
Kalman Filter ◽  
Model Predictive Control ◽  
Portfolio Optimization ◽  
Stock Returns ◽  
Predictive Control ◽  
Stock Prices ◽  
Geometric Brownian Motion ◽  
The Future ◽  
Stock Portfolio

<p style='text-indent:20px;'>A stock portfolio is a collection of assets owned by investors, such as companies or individuals. The determination of the optimal stock portfolio is an important issue for the investors. Management of investors' capital in a portfolio can be regarded as a dynamic optimal control problem. At the same time, the investors should also consider about the prediction of stock prices in the future time. Therefore, in this research, we propose Geometric Brownian Motion-Kalman Filter (GBM-KF) method to predict the future stock prices. Subsequently, the stock returns will be calculated based on the forecasting results of stock prices. Furthermore, Model Predictive Control (MPC) will be used to solve the portfolio optimization problem. It is noticeable that the management strategy of stock portfolio in this research considers the constraints on assets in the portfolio and the cost of transactions. Finally, a practical application of the solution is implemented on 3 company's stocks. The simulation results show that the performance of the proposed controller satisfies the state's and the control's constraints. In addition, the amount of capital owned by the investor as the output of system shows a significant increase.</p>

Analytical Approximations of American Call Options with Discrete Dividends

2018 ◽  
Vol 26 (3) ◽  
pp. 283-310
Author(s):  
Kwangil Bae
Keyword(s):  
Brownian Motion ◽  
Stock Prices ◽  
Stock Price ◽  
Computing Time ◽  
Option Price ◽  
Geometric Brownian Motion ◽  
Option Prices ◽  
Call Options ◽  
Analytical Approximations ◽  
Discrete Dividends

In this study, we assume that stock prices follow piecewise geometric Brownian motion, a variant of geometric Brownian motion except the ex-dividend date, and find pricing formulas of American call options. While piecewise geometric Brownian motion can effectively incorporate discrete dividends into stock prices without losing consistency, the process results in the lack of closed-form solutions for option prices. We aim to resolve this by providing analytical approximation formulas for American call option prices under this process. Our work differs from other studies using the same assumption in at least three respects. First, we investigate the analytical approximations of American call options and examine European call options as a special case, while most analytical approximations in the literature cover only European options. Second, we provide both the upper and the lower bounds of option prices. Third, our solutions are equal to the exact price when the size of the dividend is proportional to the stock price, while binomial tree results never match the exact option price in any circumstance. The numerical analysis therefore demonstrates the efficiency of our method. Especially, the lower bound formula is accurate, and it can be further improved by considering second order approximations although it requires more computing time.

scholarly journals Stock price prediction using geometric Brownian motion

2018 ◽  
Vol 974 ◽  
pp. 012047 ◽  
Author(s):  
W Farida Agustini ◽  
Ika Restu Affianti ◽  
Endah RM Putri
Keyword(s):  
Brownian Motion ◽  
Stock Price ◽  
Geometric Brownian Motion ◽  
Stock Price Prediction ◽  
Price Prediction

OPTIMAL TRADE EXECUTION UNDER GEOMETRIC BROWNIAN MOTION IN THE ALMGREN AND CHRISS FRAMEWORK

2011 ◽  
Vol 14 (03) ◽  
pp. 353-368 ◽  
Author(s):  
JIM GATHERAL ◽  
ALEXANDER SCHIED
Keyword(s):  
Brownian Motion ◽  
Stock Price ◽  
Closed Form Solution ◽  
Form Solution ◽  
Geometric Brownian Motion ◽  
Price Process ◽  
Risk Criterion ◽  
Execution Strategy ◽  
Optimal Trade Execution ◽  
Alternative Choice

With an alternative choice of risk criterion, we solve the HJB equation explicitly to find a closed-form solution for the optimal trade execution strategy in the Almgren–Chriss framework assuming the underlying unaffected stock price process is geometric Brownian motion.

scholarly journals Volatility Modelling and VaR: The Case of Bitcoin, Ether and Ripple

2020 ◽  
Vol 11 (3) ◽  
pp. 253-269
Author(s):  
Jakub Ječmínek ◽  
Gabriela Kukalová ◽  
Lukáš Moravec
Keyword(s):  
Stochastic Process ◽  
Monte Carlo Simulation ◽  
Risk Management ◽  
Monte Carlo ◽  
Brownian Motion ◽  
Value At Risk ◽  
Risk Estimation ◽  
Geometric Brownian Motion ◽  
Empirical Literature ◽  
Digital Assets

Abstract Since Bitcoin introduction in 2008, the cryptocurrency market has grown into hundreds-of-billion-dollar market. The cryptocurrency market is well known as very volatile, mainly for the fact that the cryptocurrencies have not the price to fall back upon and that anybody can join the trading (no license or approval is required). Since empirical literature suggests that GARCH-type models dominate as VaR estimators the overall objective of this paper is to perform comprehensive volatility and VaR estimation for three major digital assets and conclude which method gives the best results in terms of risk management. The methods we used are parametric (GARCH and EWMA model), non-parametric (historical VaR) and Monte Carlo simulation (given by Geometric Brownian Motion). We conclude that the best method for value-at-risk estimation for cryptocurrencies is the Monte Carlo simulation due to the heavy diffusion (stochastic) process and robustness of the results.

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