Modeling financial environments using geometric fractional Brownian motion model with long memory stochastic volatility

Modeling financial environments using geometric fractional Brownian motion model with long memory stochastic volatility

Geometric Fractional Brownian Motion (GFBM) model is widely used in financial environments. This model consists of important parameters i.e. mean, volatility, and Hurst index, which are significant to many problems in finance particularly option pricing, value at risk, exchange rate, and mortgage in...

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Main Author: Al Haqyan, Mohammed Kamel Mohammed
Format: Thesis
Language:eng
eng
eng
Published: 2018
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HG Finance
QA Mathematics
Online Access:https://etd.uum.edu.my/6895/1/DepositPermission_s93750.pdf
https://etd.uum.edu.my/6895/2/s93750_01.pdf
https://etd.uum.edu.my/6895/3/s93750_02.pdf
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institution Universiti Utara Malaysia
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language eng
eng
eng
advisor Misiran, Masnita
Omar, Zurni
topic HG Finance
QA Mathematics
spellingShingle HG Finance
QA Mathematics
Al Haqyan, Mohammed Kamel Mohammed
Modeling financial environments using geometric fractional Brownian motion model with long memory stochastic volatility
description Geometric Fractional Brownian Motion (GFBM) model is widely used in financial environments. This model consists of important parameters i.e. mean, volatility, and Hurst index, which are significant to many problems in finance particularly option pricing, value at risk, exchange rate, and mortgage insurance. Most current works investigated GFBM under the assumption of its volatility that is constant due to its simplicity. However, such assumption is normally rejected in most empirical studies. Therefore, this research develops a new GFBM model that can better describe and reflect real life situations particularly in financial scenario. All parameters involved in the developed model are estimated by using innovation algorithm. A simulation study is then conducted to determine the performance of the new model. The results of simulation reveal that the proposed estimators are efficient based on the bias, variance, and mean square error. Subsequently, two theorems on existence and uniqueness of the solution for the new model and its generalisation are constructed. The validation of the developed model was then carried out by comparing with other models in forecasting adjusted prices of Standard and Poor 500, Shanghai Stock Exchange Composite Index, and FTSE Kuala Lumpur Composite Index. Empirical studies on four selected financial applications, i.e. option pricing, value at risk, exchange rate, and mortgage insurance, indicate that the new model performs better than the existing ones. Hence, the new model has strong potential to be employed as an underlying model for any financial applications that capable of reflecting the real situation more accurately.
format Thesis
qualification_name Ph.D.
qualification_level Doctorate
author Al Haqyan, Mohammed Kamel Mohammed
author_facet Al Haqyan, Mohammed Kamel Mohammed
author_sort Al Haqyan, Mohammed Kamel Mohammed
title Modeling financial environments using geometric fractional Brownian motion model with long memory stochastic volatility
title_short Modeling financial environments using geometric fractional Brownian motion model with long memory stochastic volatility
title_full Modeling financial environments using geometric fractional Brownian motion model with long memory stochastic volatility
title_fullStr Modeling financial environments using geometric fractional Brownian motion model with long memory stochastic volatility
title_full_unstemmed Modeling financial environments using geometric fractional Brownian motion model with long memory stochastic volatility
title_sort modeling financial environments using geometric fractional brownian motion model with long memory stochastic volatility
granting_institution Universiti Utara Malaysia
granting_department Awang Had Salleh Graduate School of Arts & Sciences
publishDate 2018
url https://etd.uum.edu.my/6895/1/DepositPermission_s93750.pdf
https://etd.uum.edu.my/6895/2/s93750_01.pdf
https://etd.uum.edu.my/6895/3/s93750_02.pdf
_version_ 1747828124614131712
spelling my-uum-etd.68952021-08-09T03:48:28Z Modeling financial environments using geometric fractional Brownian motion model with long memory stochastic volatility 2018 Al Haqyan, Mohammed Kamel Mohammed Misiran, Masnita Omar, Zurni Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts and Sciences HG Finance QA Mathematics Geometric Fractional Brownian Motion (GFBM) model is widely used in financial environments. This model consists of important parameters i.e. mean, volatility, and Hurst index, which are significant to many problems in finance particularly option pricing, value at risk, exchange rate, and mortgage insurance. Most current works investigated GFBM under the assumption of its volatility that is constant due to its simplicity. However, such assumption is normally rejected in most empirical studies. Therefore, this research develops a new GFBM model that can better describe and reflect real life situations particularly in financial scenario. All parameters involved in the developed model are estimated by using innovation algorithm. A simulation study is then conducted to determine the performance of the new model. The results of simulation reveal that the proposed estimators are efficient based on the bias, variance, and mean square error. Subsequently, two theorems on existence and uniqueness of the solution for the new model and its generalisation are constructed. The validation of the developed model was then carried out by comparing with other models in forecasting adjusted prices of Standard and Poor 500, Shanghai Stock Exchange Composite Index, and FTSE Kuala Lumpur Composite Index. Empirical studies on four selected financial applications, i.e. option pricing, value at risk, exchange rate, and mortgage insurance, indicate that the new model performs better than the existing ones. Hence, the new model has strong potential to be employed as an underlying model for any financial applications that capable of reflecting the real situation more accurately. 2018 Thesis https://etd.uum.edu.my/6895/ https://etd.uum.edu.my/6895/1/DepositPermission_s93750.pdf text eng public https://etd.uum.edu.my/6895/2/s93750_01.pdf text eng public https://etd.uum.edu.my/6895/3/s93750_02.pdf text eng public Ph.D. doctoral Universiti Utara Malaysia Abidin, S. N. Z., & Jaffar, M. M. (2012). A review on Geometric Brownian Motion in forecasting the share prices in Bursa Malaysia. World Applied Sciences Journal, 17, 87-93. Abidin, S. N. Z., & Jaffar, M. M. (2014). Forecasting share prices of small size companies in bursa Malaysia using geometric Brownian motion. 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