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

✍ Scribed by Xiao-Tian Wang; En-Hui Zhu; Ming-Ming Tang; Hai-Gang Yan

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 438 KB
• Volume: 389
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2009.09.043

✦ Synopsis

This paper deals with the problem of discrete-time option pricing by the mixed Brownianfractional 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 c min (t, s t ) 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.