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Scaling and long-range dependence in option pricing III: A fractional version of the Merton model with transaction costs

Authors:	Xiao-Tian Wang Hai-Gang Yan Ming-Ming Tang En-Hui Zhu

Institution:	^aDepartment of Mathematics, South China University of Technology, Guangzhou, 510640, Guangdong, China

Abstract:	A model for option pricing of fractional version of the Merton model with ‘Hurst exponent’ H being in 1/2,1) is established with transaction costs. In particular, for H(1/2,1) the minimal price C_min(t,S_t) of an option under transaction costs is obtained, which displays that the timestep δt and the ‘Hurst exponent’ H play an important role in option pricing with transaction costs.

Keywords:	Fractional Brownian motion Transaction costs Option pricing Scaling Jump
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