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Continuous time Black–Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime

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  • Wang, Jun
  • Liang, Jin-Rong
  • Lv, Long-Jin
  • Qiu, Wei-Yuan
  • Ren, Fu-Yao
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    Abstract

    In 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 Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 391 (2012)
    Issue (Month): 3 ()
    Pages: 750-759

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    Handle: RePEc:eee:phsmap:v:391:y:2012:i:3:p:750-759

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Subdiffusion; Black–Scholes formula; Fractional Black–Scholes equation; Transaction costs;

    References

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    1. Jumarie, Guy, 2008. "Stock exchange fractional dynamics defined as fractional exponential growth driven by (usual) Gaussian white noise. Application to fractional Black-Scholes equations," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 271-287, February.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    3. Wang, Xiao-Tian, 2010. "Scaling and long range dependence in option pricing, IV: Pricing European options with transaction costs under the multifractional Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 789-796.
    4. Monoyios, Michael, 2004. "Option pricing with transaction costs using a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 889-913, February.
    5. Hayne E. Leland., 1984. "Option Pricing and Replication with Transactions Costs," Research Program in Finance Working Papers 144, University of California at Berkeley.
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