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Scaling and long-range dependence in option pricing I: Pricing European option with transaction costs under the fractional Black–Scholes model

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  • Wang, Xiao-Tian

Abstract

This paper deals with the problem of discrete time option pricing by the fractional Black–Scholes 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. The minimal price Cmin(t,St) of an option under transaction costs is obtained as timestep δt=(2π)12H(kσ)1H, which can be used as the actual price of an option. In fact, Cmin(t,St) is an adjustment to the volatility in the Black–Scholes formula by using the modified volatility σ2(2π)12−14H(kσ)1−12H to replace the volatility σ, where kσ<(π2)12, H>12 is the Hurst exponent, and k is a proportional transaction cost parameter. In addition, we also show that timestep and long-range dependence have a significant impact on option pricing.

Suggested Citation

  • Wang, Xiao-Tian, 2010. "Scaling and long-range dependence in option pricing I: Pricing European option with transaction costs under the fractional Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 438-444.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:3:p:438-444
    DOI: 10.1016/j.physa.2009.09.041
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