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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.
Volume (Year): 391 (2012)
Issue (Month): 3 ()
Contact details of provider:
Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/
Subdiffusion; Black–Scholes formula; Fractional Black–Scholes equation; Transaction costs;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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.
- Leland, Hayne E, 1985.
" Option Pricing and Replication with Transactions Costs,"
Journal of Finance,
American Finance Association, vol. 40(5), pages 1283-1301, December.
- Hayne E. Leland., 1984. "Option Pricing and Replication with Transactions Costs," Research Program in Finance Working Papers 144, University of California at Berkeley.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.