Scaling and long-range dependence in option pricing II: Pricing European option with transaction costs under the mixed Brownian–fractional Brownian model

Xiao-Tian Wang, En-Hui Zhu, Ming-Ming Tang and Hai-Gang Yan

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 3, 445-451

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.

Keywords: Mixed Brownian–fractional Brownian model; Option pricing; Transaction costs; Delta-hedging; Scaling (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (25)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:3:p:445-451

DOI: 10.1016/j.physa.2009.09.043

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