scholarly journals Geometric Brownian Motion in Stock Prices

2019 ◽  
Vol 1377 ◽  
pp. 012016
Author(s):  
K Suganthi ◽  
G Jayalalitha
Keyword(s):  
Brownian Motion ◽  
Stock Prices ◽  
Geometric Brownian Motion

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>

scholarly journals Comparison of Stochastic Forecasting Models

2021 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Brownian Motion ◽  
Stock Prices ◽  
Absolute Error ◽  
Geometric Brownian Motion ◽  
Time Dependent ◽  
Confidence Bounds ◽  
History Of ◽  
Brownian Motion Model ◽  
Stochastic Forecasting ◽  
Two Parameters

In this work, we compare several stochastic forecasting techniques like Stochastic Differential Equations (SDE), ARIMA, the Bayesian filter, Geometric Brownian motion (GBM), and the Kalman filter. We use historical daily stock prices of Microsoft (MSFT), Target (TGT) and Tesla (TSLA) and apply all algorithms to try to predict 54 days ahead. We find that there are instances in which all algorithms do well, or do poorly. We find that all three stocks have a strong auto-correlation and a high Hurst factor which shows that it is possible to predict future prices based on a short history of past prices. In our geometric Brownian motion model, we have two parameters for drift and diffusion which are not time dependent. In our more general SDE model (TDNGBM), we have time-dependent drift and time-dependent diffusion terms which makes it more effective than GBM. We measure all algorithms on the correlation between the predicted and actual values, the mean absolute error (MAE) and also the confidence bounds generated by the methods. Confidence intervals are more important than point forecasts, and we see that TDNGBM and ARIMA produce good bounds.

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 Fuzzy Time Series and Geometric Brownian Motion in Forecasting Stock Prices in Bursa Malaysia

2019 ◽  
Vol 14 (2) ◽  
pp. 240-250
Author(s):  
Nor Hayati Shafii ◽  
Nur Ezzati Dayana Mohd Ramli ◽  
Rohana Alias ◽  
Nur Fatihah Fauzi
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Stock Market ◽  
Stock Prices ◽  
Stock Exchange ◽  
Investment Decisions ◽  
Geometric Brownian Motion ◽  
Fuzzy Time Series ◽  
Good Information ◽  
The Mean

Every country has its own stock market exchange, which is a platform to raise capital and is a place where shares of listed company are traded. Bursa Malaysia is a stock exchange of Malaysia and it is previously known as Kuala Lumpur Stock Exchange. All over the world, including Malaysia, it is common for investors or traders to face some loss due to wrong investment decisions. According to the conventional financial theory, there are so many reasons that can lead to bad investment decisions. One of them is confirmation bias where an investor has a preconceived notion about an investment without a good information and knowledge. In this paper, we study the best way to provide good information for investors in helping them make the right decisions and not to fall prey to this behavioral miscue. Two models for forecasting stock prices data are employed, namely, Fuzzy Time Series (FTS) and Geometric Brownian Motion (GBM). This study used a secondary data consisting of AirAsia Berhad daily stock prices for a duration of 20 weeks from January 2015 to May 2015. The 16-weeks data from January to April 2015 was used to forecast the stock prices for the 4-weeks of May 2015. The results showed that FTS has the lowest values of the Mean Absolute Percentage Error (MAPE) and the Mean Square Error (MSE), which are 1.11% and MYR20.0011, respectively. For comparison, for GBM, the MAPE is 1.53% and the MSE is MYR2 0.0017. The findings imply that the FTS model provides a more accurate forecast of stock prices. Keywords: Forecasted values, stock market, Fuzzy Time Series, Geometric Brownian Motion

scholarly journals Forecasting Cyclical and Non-cyclical Stock Prices on the Stock Exchange of Thailand

2021 ◽  
Vol 17 (5) ◽  
pp. 550-565
Author(s):  
Rapin Sunthornwat ◽  
Yupaporn Areepong
Keyword(s):  
Decision Making ◽  
Brownian Motion ◽  
Stock Prices ◽  
Stock Exchange ◽  
Geometric Brownian Motion ◽  
Percentage Error ◽  
Initial Value ◽  
Minimum Error ◽  
Stock Exchange Of Thailand ◽  
And Performance

Forecasting is an important role in organizations for decision making and planning. This research is to forecast the cyclical and non-cyclical weekly stock prices on the Stock Exchange of Thailand by using the models of Geometric Brownian motion, Fourier’s series, and Cauchy initial value problem. The accuracy and performance of the models are based on the minimum root mean squared percentage error which is the error between actual and forecasted stock prices. The results showed that Geometric Brownian motion is suitable for forecasting both cyclical and non-cyclical stock prices because of minimum error. Moreover, the confidence intervals of forecasted stock prices are demonstrated. Therefore, Geometric Brownian motion should be selected to describe the movement of stock prices in Thailand.

scholarly journals Analysing the Nepali Stock Market with Stochastic Models

2016 ◽  
Vol 1 (1) ◽  
Author(s):  
Karan Singh Thagunna ◽  
Radal M Lochowski
Keyword(s):  
Brownian Motion ◽  
Stock Market ◽  
Diffusion Model ◽  
Stock Prices ◽  
Jump Diffusion ◽  
Efficient Market Hypothesis ◽  
Geometric Brownian Motion ◽  
Brownian Motion Model ◽  
Jump Diffusion Model ◽  
Daily Returns

In this article we analyse the behaviour of the Nepali stock market and movements of stock prices of selected companies using (i) Efficient Market Hypothesis (EMH) (ii) geometric Brownian motion model (gBm) and (iii) Merton’s jump-diffusion model. Using the daily returns of the NEPSE index and the daily returns of stock prices of selected companies we estimate the geometric Brownian motion model and Merton’s jump-diffusion model. Further, we compare both models to identify the best fit for the Nepali stock market data. Keywords: Black-Scholes model, Efficient Market Hypothesis, geometric Brownian motion, Merton’s jump-diffusion Model, Variance Ratio Test

scholarly journals Geometric Brownian Motion and Value at Risk For Analysis Stock Price Of Bumi Serpong Damai Ltd

2021 ◽  
Vol 1 (1) ◽  
pp. 11-21
Author(s):  
Trimono Trimono ◽  
Di Asih I Maruddani ◽  
Prisma Hardi Aji Riyantoko ◽  
I Gede Susrama Mas Diyasa
Keyword(s):  
Brownian Motion ◽  
Capital Market ◽  
Confidence Level ◽  
Stock Prices ◽  
Value At Risk ◽  
Stock Price ◽  
Risk Measure ◽  
Geometric Brownian Motion ◽  
Financial Assets ◽  
The People

Investment is one of the activities that last actually attractive to the people of Indonesia. One of the most widely traded financial assets in the capital market is stocks. Stock prices frequently experience challenges to predict changes, so they can increase or decrease at any time. One method that can be applied to predict stock prices is GBM. Then, the risk can be measured using the VaR risk measure. The GBM model is determined to be accurate in predicting the stock price of BSDE.JK, with a MAPE value of 5.17%. By using VaR-HS and VaR CFE, the prediction of risk of loss at the 95% confidence level for the period 06/07/21 is -0.0597 and -0.0623

Stochastic Forecasting of Stock Prices in Nigeria: Application of Geometric Brownian Motion Model

2021 ◽  
Vol 6 (2) ◽  
pp. 1-35
Author(s):  
Adolphus Joseph Toby ◽  
Samuel Azubuike Agbam
Keyword(s):  
Brownian Motion ◽  
Stock Prices ◽  
Stock Exchange ◽  
Investment Strategy ◽  
Time Frame ◽  
Geometric Brownian Motion ◽  
Percentage Error ◽  
Unique Contribution ◽  
Holding Period ◽  
Stochastic Forecasting

Purpose:  The purpose of the study is to model and simulate the trends and behavioral patterns in The Nigerian Stock Market and hence predict the future stock prices within the Geometric Brownian Motion (GBM) framework. Methodology: The methodology involves a comparison of forecasted daily closing prices to actual prices in order to evaluate the accuracy of the prediction model. Based on the model assumptions of the GBM with drift: continuity, normality and Markov tendency, the study investigated four years (2015 - 2018) of historical closing prices of ten stocks listed on The Nigerian Stock Exchange. The sample for this study is based on the most continuously traded stocks. Findings: The results show that in the simulation there are some actual stock prices located outside trajectory realization that may be from GBM model. Thus, the model did not predict accurately the price behavior of some of the listed stocks.  The predictive power of the model is declining towards the longer the evaluated time frame proven by the higher value of the mean absolute percentage error. The value of the MAPE is 50% and below for the one- to two-year holding periods, and above 50% for the three-year holding period. Unique Contribution to theory, Practice and Policy:  The MAPE and directional prediction accuracy method provide support that over short periods the GBM model is accurate. Meaning that the GBM is a reasonable predictive model for one or two years, but for three years, therefore, it is an inaccurate predictor. It is recommended that the technical analyst whose primary motive is to make gain at the expense of other participants should identify high volatile portfolio in any holding period for effective prediction Investors with long-range holding position as investment strategy should concentrate more on low capitalized stocks rather than stocks with large market capitalization. This is a unique contribution to theory, practice and policy. 

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