Estimating dynamic geometric fractional brownian motion and its application to long-memory option pricing
Geometric fractional Brownian motion (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 t...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
2012
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| Online Access: | http://hdl.handle.net/20.500.11937/11322 |
| _version_ | 1848747774647992320 |
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| author | Misiran, M. Zudi, L. Teo, Kok Lay Grace, A. |
| author_facet | Misiran, M. Zudi, L. Teo, Kok Lay Grace, A. |
| author_sort | Misiran, M. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Geometric fractional Brownian motion (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 s 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 s 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. |
| first_indexed | 2025-11-14T06:54:30Z |
| format | Journal Article |
| id | curtin-20.500.11937-11322 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T06:54:30Z |
| publishDate | 2012 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-113222017-01-30T11:24:03Z Estimating dynamic geometric fractional brownian motion and its application to long-memory option pricing Misiran, M. Zudi, L. Teo, Kok Lay Grace, A. Geometric fractional Brownian motion (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 s 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 s 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 Journal Article http://hdl.handle.net/20.500.11937/11322 restricted |
| spellingShingle | Misiran, M. Zudi, L. Teo, Kok Lay Grace, A. 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 |
| url | http://hdl.handle.net/20.500.11937/11322 |