Continuous time Black–Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime
AbstractIn this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(Sα(t)), 0<α<1, here dX(τ)=μX(τ)(dτ)2H+σX(τ)dBH(τ), as a model of asset prices, which captures the subdiffusive characteristic of financial markets. We find the corresponding subdiffusive Black–Scholes equation and the Black–Scholes formula for the fair prices of European option, the turnover and transaction costs of replicating strategies. We also give the total transaction costs.
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Bibliographic InfoArticle provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.
Volume (Year): 391 (2012)
Issue (Month): 3 ()
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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/
Subdiffusion; Black–Scholes formula; Fractional Black–Scholes equation; Transaction costs;
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