Journal of Applied Mathematics

Asian Option Pricing with Monotonous Transaction Costs under Fractional Brownian Motion

Di Pan, Shengwu Zhou, Yan Zhang, and Miao Han

Full-text: Open access

Abstract

Geometric-average Asian option pricing model with monotonous transaction cost rate under fractional Brownian motion was established. The method of partial differential equations was used to solve this model and the analytical expressions of the Asian option value were obtained. The numerical experiments show that Hurst exponent of the fractional Brownian motion and transaction cost rate have a significant impact on the option value.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 352021, 6 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808284

Digital Object Identifier
doi:10.1155/2013/352021

Mathematical Reviews number (MathSciNet)
MR3138986

Zentralblatt MATH identifier
06950629

Citation

Pan, Di; Zhou, Shengwu; Zhang, Yan; Han, Miao. Asian Option Pricing with Monotonous Transaction Costs under Fractional Brownian Motion. J. Appl. Math. 2013 (2013), Article ID 352021, 6 pages. doi:10.1155/2013/352021. https://projecteuclid.org/euclid.jam/1394808284


Export citation

References

  • E. E. Peters, “Fractal structure in the capital markets,” Financial Analyst Journal, vol. 45, no. 4, pp. 32–37, 1989.
  • T. E. Duncan, Y. Hu, and B. Pasik-Duncan, “Stochastic calculus for fractional Brownian motion. I. Theory,” SIAM Journal on Control and Optimization, vol. 38, no. 2, pp. 582–612, 2000.
  • F. Biagini, Y. Hu, B. ${\text{\O}}$ksendal, and T. Zhang, Stochastic Calculus for Fractional Brownian Motion and Applications, 2008.
  • E. Alos, O. Mazet, and D. Nualart, “Stochastic calculus with res-pect to the fractional Brownian motion,” Stochastic Processes and Their Applications, vol. 86, pp. 121–139, 2000.
  • C. Bender, “An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter,” Stochastic Processes and their Applications, vol. 104, no. 1, pp. 81–106, 2003.
  • C. Necula, “Option pricing in a fractional Brownian motion environment,” vol. 27, pp. 8079–8089, Academy of Economic Studies Bucharest, Romania, Preprint, Academy of Economic Studies, Bucharest, Romania, 2002.
  • H. E. Leland, “Option pricing and replication with transactions costs,” The Journal of Finance, vol. 40, no. 5, pp. 1283–1301, 1985.
  • G. Barles and H. M. Soner, “Option pricing with transaction costs and a nonlinear Black-Scholes equation,” Finance and Stochastics, vol. 2, no. 4, pp. 369–397, 1998.
  • P. Amster, C. G. Averbuj, M. C. Mariani, and D. Rial, “A Black-Scholes option pricing model with transaction costs,” Journal of Mathematical Analysis and Applications, vol. 303, no. 2, pp. 688–695, 2005.
  • H.-K. Liu and J.-J. Chang, “A closed-form approximation for the fractional Black-Scholes model with transaction costs,” Computers & Mathematics with Applications, vol. 65, no. 11, pp. 1719–1726, 2013.
  • J. Wang, J.-R. Liang, L.-J. Lv, W.-Y. Qiu, and F.-Y. Ren, “Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime,” Physica A, vol. 391, no. 3, pp. 750–759, 2012.
  • B. B. Mandelbrot, Fractals and Scaling in Finance: Discontinuity and Concentration, Springer, New York, NY, USA, 1997.