Journal of East China Normal University(Natural Sc ›› 2018, Vol. 2018 ›› Issue (4): 47-58.doi: 10.3969/j.issn.1000-5641.2018.04.005

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Pricing of lookback options under a mixed fractional Brownian movement

CHEN Hai-zhen, ZHOU Sheng-wu, SUN Xiang-yan   

  1. Department of Mathematics, China University of Mining and Technology, Xuzhou Jiangsu 221116, China
  • Received:2017-07-10 Online:2018-07-25 Published:2018-07-19

Abstract: This paper studied the pricing of European lookback options when the underlying asset followed a mixed fractional Brownian movement and the transaction costs were considered. Firstly, the nonlinear partial differential equation and its boundary condition were obtained using the hedging principle under the model. Secondly, the partial differential equation was reduced using variable substitution. Next, we found its numerical solution by constructing a Crank-Nicolson format. Lastly, the convergence of the numerical scheme was discussed. We also discussed the influence of the transaction fee ratio, Hurst index, and so on.

Key words: mixed fractional Brownian movement, transaction fee, European lookback option, Crank-Nicolson format

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