title: Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion.
abstract: The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland's hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, the effectiveness of the proposed form is verified through a numerical example. Meanwhile, the impact of transaction cost rate and volatility on lookback option value is discussed.
authors.affiliation: College of Sciences, China University of Mining and Technology, Xuzhou 221116, China.
authors.forename: Jiao-Jiao
authors.initials: JJ
authors.lastname: Sun
authors.affiliation: College of Sciences, China University of Mining and Technology, Xuzhou 221116, China.
authors.forename: Shengwu
authors.initials: S
authors.lastname: Zhou
authors.affiliation: College of Sciences, China University of Mining and Technology, Xuzhou 221116, China.
authors.forename: Yan
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: College of Sciences, China University of Mining and Technology, Xuzhou 221116, China.
authors.forename: Miao
authors.initials: M
authors.lastname: Han
authors.affiliation: College of Sciences, China University of Mining and Technology, Xuzhou 221116, China.
authors.forename: Fei
authors.initials: F
authors.lastname: Wang