Estimating Dynamic Geometric Fractional Brownian Motion and Its Application to Long-Memory Option Pricing
Geometric fractional Brownianmotion (GFBM) is an extended dynamic model of the traditional geometric Brownian motion, and has been used in characterizing the long term memory dynamic behavior of financial time series and in pricing long-memory options. A crucial problem in its applications is how th...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Dynamic Publishers, Inc.
2012
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| Online Access: | https://repo.uum.edu.my/id/eprint/30833/1/DSA%2021%202012%2049-66.pdf |
| _version_ | 1803629987596599296 |
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| author | Misiran, Masnita Lu, Zudi Kok Lay, Teo Aw, Grace |
| author_facet | Misiran, Masnita Lu, Zudi Kok Lay, Teo Aw, Grace |
| author_sort | Misiran, Masnita |
| collection | UUM |
| description | Geometric fractional Brownianmotion (GFBM) is an extended dynamic model of the traditional geometric Brownian motion, and has been used in characterizing the long term memory dynamic behavior of financial time series and in pricing long-memory options. A crucial problem in its applications is how the unknown parameters in the model are to be estimated. In this paper, we study the problem of estimating the unknown parameters, which are the drift μ, volatility _ and Hurst index H, involved in the GFBM, based on discrete-time observations. We propose a complete maximum likelihood estimation approach, which enables us not only to derive the estimators of μ and _2, but also the estimate of the long memory parameter, H, simultaneously, for risky assets in the dynamic fractional Black-Scholes market governed by GFBM. Simulation outcomes illustrate that our methodology is statistically efficient and reliable. Empirical application to stock exchange index with European option pricing under GFBM is also demonstrated |
| first_indexed | 2024-07-04T06:46:35Z |
| format | Article |
| id | uum-30833 |
| institution | Universiti Utara Malaysia |
| language | English |
| last_indexed | 2024-07-04T06:46:35Z |
| publishDate | 2012 |
| publisher | Dynamic Publishers, Inc. |
| record_format | dspace |
| spelling | uum-308332024-05-29T11:23:58Z https://repo.uum.edu.my/id/eprint/30833/ Estimating Dynamic Geometric Fractional Brownian Motion and Its Application to Long-Memory Option Pricing Misiran, Masnita Lu, Zudi Kok Lay, Teo Aw, Grace QA Mathematics Geometric fractional Brownianmotion (GFBM) is an extended dynamic model of the traditional geometric Brownian motion, and has been used in characterizing the long term memory dynamic behavior of financial time series and in pricing long-memory options. A crucial problem in its applications is how the unknown parameters in the model are to be estimated. In this paper, we study the problem of estimating the unknown parameters, which are the drift μ, volatility _ and Hurst index H, involved in the GFBM, based on discrete-time observations. We propose a complete maximum likelihood estimation approach, which enables us not only to derive the estimators of μ and _2, but also the estimate of the long memory parameter, H, simultaneously, for risky assets in the dynamic fractional Black-Scholes market governed by GFBM. Simulation outcomes illustrate that our methodology is statistically efficient and reliable. Empirical application to stock exchange index with European option pricing under GFBM is also demonstrated Dynamic Publishers, Inc. 2012 Article PeerReviewed application/pdf en https://repo.uum.edu.my/id/eprint/30833/1/DSA%2021%202012%2049-66.pdf Misiran, Masnita and Lu, Zudi and Kok Lay, Teo and Aw, Grace (2012) Estimating Dynamic Geometric Fractional Brownian Motion and Its Application to Long-Memory Option Pricing. Dynamic Systems and Applications, 21. pp. 49-66. ISSN 1056-2176 https://espace.curtin.edu.au/handle/20.500.11937/11322 |
| spellingShingle | QA Mathematics Misiran, Masnita Lu, Zudi Kok Lay, Teo Aw, Grace Estimating Dynamic Geometric Fractional Brownian Motion and Its Application to Long-Memory Option Pricing |
| title | Estimating Dynamic Geometric Fractional Brownian Motion and Its Application to Long-Memory Option Pricing |
| title_full | Estimating Dynamic Geometric Fractional Brownian Motion and Its Application to Long-Memory Option Pricing |
| title_fullStr | Estimating Dynamic Geometric Fractional Brownian Motion and Its Application to Long-Memory Option Pricing |
| title_full_unstemmed | Estimating Dynamic Geometric Fractional Brownian Motion and Its Application to Long-Memory Option Pricing |
| title_short | Estimating Dynamic Geometric Fractional Brownian Motion and Its Application to Long-Memory Option Pricing |
| title_sort | estimating dynamic geometric fractional brownian motion and its application to long memory option pricing |
| topic | QA Mathematics |
| url | https://repo.uum.edu.my/id/eprint/30833/1/DSA%2021%202012%2049-66.pdf |
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