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Mathematical Problems in Engineering
Volume 2016, Article ID 6817483, 8 pages
Research Article

Dynamic Hedging Based on Fractional Order Stochastic Model with Memory Effect

1Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
2School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China
3School of Finance, Zhongnan University of Economics and Law, Wuhan 430073, China
4Wuhan Technology and Business University, Wuhan 430065, China

Received 4 April 2016; Revised 18 May 2016; Accepted 22 May 2016

Academic Editor: Josè A. Tenereiro Machado

Copyright © 2016 Qing Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Many researchers have established various hedge models to get the optimal hedge ratio. However, most of the hedge models only discuss the discrete-time processes. In this paper, we construct the minimum variance model for the estimation of the optimal hedge ratio based on the stochastic differential equation. At the same time, also by considering memory effects, we establish the continuous-time hedge model with memory based on the fractional order stochastic differential equation driven by a fractional Brownian motion to estimate the optimal dynamic hedge ratio. In addition, we carry on the empirical analysis to examine the effectiveness of our proposed hedge models from both in-sample test and out-of-sample test.