Pricing Double Barrier Parisian Option Using Finite Difference

Xuemei Gao

South Western University of Finance and Economics, Chengdu, China.

DOI: 10.4236/jfrm.2013.24011                

Abstract

In this paper, we price the valuation of double barrier Parisian options, under the Black-Scholes framework. The approach is based on fundamental partial differential equations. We reduce the dimension of partial differential equations，then using finite difference scheme to solve the partial differential equations.

Keywords

Black-Scholes Model; Double Barrier; Parisian Options; Finite Difference Scheme

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Baldi, P. Caramellino, L., & Iovino, M. G. (2000). Pricing complex barrier options with general features using sharp large deviation estimates. In Monte Carlo and quasi-Monte Carlo methods in scientific computing (3rd ed., pp. 149-162). Claremont, CA: Springer.
[2]	Avellaneda, M., & Wu, L. (1999). Pricing parisian-style options with a lattice method. International Journal of Theoretical and Applied Finance, 2, 1-16. http://dx.doi.org/10.1142/S0219024999000029
[3]	Zhu, S. P., & Chen, W. T. (2013). Pricing Parisian and Parasian options analytically. Journal of Economic Dynamics and Control, 37, 875896. http://dx.doi.org/10.1016/j.jedc.2012.12.005
[4]	Wilmott, P. (1998). Derivatives: The theory and practice of financial engineering (University ed). Hoboken, NJ: Wiley.
[5]	Haber, R. J., Schonbucher, P. J., & Wilmott, P. (1999). Pricing Parisian options. The Journal of Derivatives, 6, 71-79.
[6]	Chesney, M., Jeanblanc-Picqué, M., & Yor, M., (1997). Brownian excursions and Parisian barrier options. Advances in Applied Microbiology, 29, 165-184.
[7]	Labart, C. & Lelong, J. (2009). Pricing double barrier Parisian options using laplace transforms. International Journal of Theoretical and Applied Finance, 12. http://dx.doi.org/10.1142/S0219024909005154
[8]	Simon, B. (2000). A Faynman-Kac formula for unbounded semigroups. Canadian Mathematical Society Conference Proceedings, 40, 317321.