JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (4): 100-110.doi: 10.6040/j.issn.1671-9352.0.2021.622

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Pricing and simulation of lookback options under the mixed sub-fractional jump-diffusion model

AN Xiang, GUO Jing-jun*   

  1. School of Statistics, Lanzhou University of Finance and Economics, Lanzhou 730020, Gansu, China
  • Published:2022-03-29

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Abstract: The pricing model of European lookback options with transaction costs is established based on the mixed sub-fractional Brownian motion and Poisson process. Firstly, the nonlinear partial differential equation satisfied by the price of the option is obtained using the Delta hedging principle, and its numerical solution is obtained by constructing a Crank-Nicolson format. Secondly, the validity of the numerical method is verified, and the effects of transaction costs, volatility and risk-free interest rate on the value of the option are respectively discussed. Finally, the daily closing price of Shanghai Pudong Development Bank is selected for the simulation, and the results show that the simulated price based on the mixed sub-fractional jump-diffusion model is closer to the real value of the stock, and can better reflect the overall stock trend.

Key words: mixed sub-fractional Brownian motion, jump-diffusion model, European lookback options, transaction costs, Crank-Nicolson format

CLC Number: 

  • O211.6
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