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Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion
Jiao-Jiao Sun1, Shengwu Zhou1, Yan Zhang1
1College of Sciences, China University of Mining and Technology, Xuzhou 221116, China.
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.
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