Scaling and long-range dependence in option pricing II: Pricing European option with transaction costs under the mixed Brownian–fractional Brownian model |
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Authors: | Xiao-Tian Wang En-Hui Zhu Ming-Ming Tang Hai-Gang Yan |
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Institution: | a Department of Mathematics, South China University of Technology, Guangzhou 510640, PR China |
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Abstract: | This paper deals with the problem of discrete-time option pricing by the mixed Brownian–fractional Brownian model with transaction costs. By a mean-self-financing delta hedging argument in a discrete-time setting, a European call option pricing formula is obtained. In particular, the minimal pricing cmin(t,st) of an option under transaction costs is obtained, which shows that timestep δt and Hurst exponent H play an important role in option pricing with transaction costs. In addition, we also show that there exists fundamental difference between the continuous-time trade and discrete-time trade and that continuous-time trade assumption will result in underestimating the value of a European call option. |
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Keywords: | Mixed Brownian– fractional Brownian model Option pricing Transaction costs Delta-hedging Scaling |
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