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    Estimating dynamic geometric fractional brownian motion and its application to long-memory option pricing

    Access Status
    Fulltext not available
    Authors
    Misiran, M.
    Zudi, L.
    Teo, Kok Lay
    Grace, A.
    Date
    2012
    Type
    Journal Article
    
    Metadata
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    Citation
    Misiran, M. and Zudi, L. and Teo, K.L. and Grace, A. 2012. Estimating dynamic geometric fractional brownian motion and its application to long-memory option pricing. Dynamic Systems and Applications. 21 (1): pp. 49-66.
    Source Title
    Dynamic Systems and Applications
    ISSN
    1056-2176
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/11322
    Collection
    • Curtin Research Publications
    Abstract

    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.

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