Estimation of geometric Brownian motion model with a t-distribution–based particle filter
Orientation: Geometric Brownian motion (GBM) model basically suggests whether the distribution of asset returns is normal or lognormal. However, many empirical studies have revealed that return distributions are usually not normal. These studies, time and again, discover evidence of non-normality, s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AOSIS
2019-02-01
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| Series: | Journal of Economic and Financial Sciences |
| Subjects: | |
| Online Access: | https://jefjournal.org.za/index.php/jef/article/view/159 |
| _version_ | 1818340373128282112 |
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| author | Bridget Nkemnole Olaide Abass |
| author_facet | Bridget Nkemnole Olaide Abass |
| author_sort | Bridget Nkemnole |
| collection | DOAJ |
| description | Orientation: Geometric Brownian motion (GBM) model basically suggests whether the distribution of asset returns is normal or lognormal. However, many empirical studies have revealed that return distributions are usually not normal. These studies, time and again, discover evidence of non-normality, such as heavy tails and excess kurtosis.
Research purpose: This work was aimed at analysing the GBM with a sequential Monte Carlo (SMC) technique based on t-distribution and compares the distribution with normal distribution.
Motivation for the study: The SMC or particle filter based on the t-distribution for the GBM model, which involves randomness, volatility and drift, can precisely capture the aforementioned statistical characteristics of return distributions and can predict the random changes or fluctuation in stock prices.
Research approach/design and method: The particle filter based on the t-distribution is developed to estimate the random effects and parameters for the extended model; the mean absolute percentage error (MAPE) were calculated to compare distribution fit. Distribution performance was assessed through simulation study and real data.
Main findings: Results show that the GBM model based on student’s t-distribution is empirically more successful than the normal distribution.
Practical/managerial implications: The proposed model which is heavier tailed than the normal does not only provide an approximate solution to non-normal estimation problem.
Contribution/value-add: The GBM model based on student’s t-distribution establishes an efficient structure for GBM and volatility modelling. |
| first_indexed | 2024-12-13T15:41:52Z |
| format | Article |
| id | doaj.art-70bbf20a0d114955960adf1541c32444 |
| institution | Directory Open Access Journal |
| issn | 1995-7076 2312-2803 |
| language | English |
| last_indexed | 2024-12-13T15:41:52Z |
| publishDate | 2019-02-01 |
| publisher | AOSIS |
| record_format | Article |
| series | Journal of Economic and Financial Sciences |
| spelling | doaj.art-70bbf20a0d114955960adf1541c324442022-12-21T23:39:48ZengAOSISJournal of Economic and Financial Sciences1995-70762312-28032019-02-01121e1e910.4102/jef.v12i1.159345Estimation of geometric Brownian motion model with a t-distribution–based particle filterBridget Nkemnole0Olaide Abass1Department of Mathematics, University of LagosDepartment of Computer Sciences, University of LagosOrientation: Geometric Brownian motion (GBM) model basically suggests whether the distribution of asset returns is normal or lognormal. However, many empirical studies have revealed that return distributions are usually not normal. These studies, time and again, discover evidence of non-normality, such as heavy tails and excess kurtosis. Research purpose: This work was aimed at analysing the GBM with a sequential Monte Carlo (SMC) technique based on t-distribution and compares the distribution with normal distribution. Motivation for the study: The SMC or particle filter based on the t-distribution for the GBM model, which involves randomness, volatility and drift, can precisely capture the aforementioned statistical characteristics of return distributions and can predict the random changes or fluctuation in stock prices. Research approach/design and method: The particle filter based on the t-distribution is developed to estimate the random effects and parameters for the extended model; the mean absolute percentage error (MAPE) were calculated to compare distribution fit. Distribution performance was assessed through simulation study and real data. Main findings: Results show that the GBM model based on student’s t-distribution is empirically more successful than the normal distribution. Practical/managerial implications: The proposed model which is heavier tailed than the normal does not only provide an approximate solution to non-normal estimation problem. Contribution/value-add: The GBM model based on student’s t-distribution establishes an efficient structure for GBM and volatility modelling.https://jefjournal.org.za/index.php/jef/article/view/159Geometric Brownian motionstudent-t distributionnormal distributiondriftvolatilityparticle filter |
| spellingShingle | Bridget Nkemnole Olaide Abass Estimation of geometric Brownian motion model with a t-distribution–based particle filter Journal of Economic and Financial Sciences Geometric Brownian motion student-t distribution normal distribution drift volatility particle filter |
| title | Estimation of geometric Brownian motion model with a t-distribution–based particle filter |
| title_full | Estimation of geometric Brownian motion model with a t-distribution–based particle filter |
| title_fullStr | Estimation of geometric Brownian motion model with a t-distribution–based particle filter |
| title_full_unstemmed | Estimation of geometric Brownian motion model with a t-distribution–based particle filter |
| title_short | Estimation of geometric Brownian motion model with a t-distribution–based particle filter |
| title_sort | estimation of geometric brownian motion model with a t distribution based particle filter |
| topic | Geometric Brownian motion student-t distribution normal distribution drift volatility particle filter |
| url | https://jefjournal.org.za/index.php/jef/article/view/159 |
| work_keys_str_mv | AT bridgetnkemnole estimationofgeometricbrownianmotionmodelwithatdistributionbasedparticlefilter AT olaideabass estimationofgeometricbrownianmotionmodelwithatdistributionbasedparticlefilter |