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

Xiao-Tian Wang

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 3, 438-444

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.

Keywords: Delta-hedging; Fractional Black–Scholes model; Transaction costs; Option pricing; Scaling (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (32)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:3:p:438-444

DOI: 10.1016/j.physa.2009.09.041

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