Development of modified Geometric Brownian Motion models by using stock price data and basic statistics

2009 ◽  
Vol 71 (12) ◽  
pp. e1203-e1208 ◽  
Author(s):  
G.S. Ladde ◽  
Ling Wu
2021 ◽  
Vol 2084 (1) ◽  
pp. 012012
Author(s):  
Tiara Shofi Edriani ◽  
Udjianna Sekteria Pasaribu ◽  
Yuli Sri Afrianti ◽  
Ni Nyoman Wahyu Astute

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.


2018 ◽  
Vol 26 (3) ◽  
pp. 283-310
Author(s):  
Kwangil Bae

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.


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