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.

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

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. 

scholarly journals Evaluation of an iron ore price forecast using a geometric Brownian motion model

2019 ◽  
Vol 72 (1 suppl 1) ◽  
pp. 9-15 ◽  
Author(s):  
André Lubene Ramos ◽  
Douglas Batista Mazzinghy ◽  
Viviane da Silva Borges Barbosa ◽  
Michel Melo Oliveira ◽  
Gilberto Rodrigues da Silva
Keyword(s):  
Brownian Motion ◽  
Iron Ore ◽  
Geometric Brownian Motion ◽  
Motion Model ◽  
Price Forecast ◽  
Brownian Motion Model

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>

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