Geometric Fractional Brownian Motion Perturbed by Fractional Ornstein-Uhlenbeck Process and Application on KLCI Option Pricing - Open Access Library Journal

OALibJ > Vol.3 No.8, August 2016

Geometric Fractional Brownian Motion Perturbed by Fractional Ornstein-Uhlenbeck Process and Application on KLCI Option Pricing ()

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DOI: 10.4236/oalib.1102863 1,469 Downloads 2,684 Views Citations

Author(s)

Mohammed Alhagyan^1,2*, Masnita Misiran¹, Zurni Omar¹

Affiliation(s)

¹Department of Mathematics and Statistics, School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, Kedah, Malaysia.
²Department of Mathematics, Community College in Al-Aflaj, Sattam University, Al Kharj, KSA.

ABSTRACT

This paper presents an enhanced model of geometric fractional Brownian motion where its volatility is assumed to be stochastic volatility model that obeys fractional Ornstein-Uhlenbeck process. The method of estimation for all parameters (α, β, m, μ, H1, and H2) in this model is derived. We calculated the value of European call option using the estimates based on the methods of Masnita [1] [2] and Kukush [3], traditional Black-Scholes European option price, in addition to proposed model in order to make comparison study.

KEYWORDS

Geometric Fractional Brownian Motion, Fractional Ornstein-Uhlenbeck Process, Long Memory Stochastic Volatility, Innovation Algorithm, Constraint Transcription Method, Segmentation, Option Pricing, KLCI

Share and Cite:

Alhagyan, M. , Misiran, M. and Omar, Z. (2016) Geometric Fractional Brownian Motion Perturbed by Fractional Ornstein-Uhlenbeck Process and Application on KLCI Option Pricing. Open Access Library Journal, 3, 1-12. doi: 10.4236/oalib.1102863.

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