Solution of Black-Scholes Equation on Barrier Option

Authors

  • S. Meena Research & Development Centre, Bharathiar University, Coimbatore 641046, Tamilnadu
  • J. Vernold Vivin Department of Mathematics, University College of Engineering Nagercoil, (Anna University Constituent College), Nagercoil 629004, Tamilnadu

DOI:

https://doi.org/10.26713/jims.v9i3.939

Keywords:

European option, Barrier option, Black Scholes equation, Co-semigroups, Mellin transform

Abstract

In this article, a solution of the Black-Scholes partial differential equation corresponding to barrier options is proposed. Semigroup theory techniques and Mellin transform method are used to discuss its solution.

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References

F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy 81 (1973), 637 – 654.

C. Chilarescu, A. Pogan and C. Preda, A generalised solution of the Black-Scholes partial differential equation, Differential Equations and Application 5 (2007), 29 – 37.

D.I. Cruz-Baez and J.M. Gonzalez-Rodriguez, Semigroup theory applied to options, Journal of Applied Mathematics 2(3) (2002), 131 – 139.

K.J. Engel and R. Nagel, One Parameter Semigroups for Linear Evolution Equations, Springer, New York (1999).

T. Evan, The Black-Scholes model and extensions, preprint (2010).

F. Lin Cheng, Mellin transform solution for the model of European option, in: EMEIT. IEEE, 329 – 331 (2011).

R. Panini and R.P. Srivastav, Option pricing with Mellin transforms, Mathematical and Computer Modelling 40(1-2) (2004), 43 – 56.

M.R. Rodrigo and R.S. Mamon, An application of Mellin transform techniques to a Black-Scholes equation problem, Analysis and Applications 5(01) (2007), 51 – 56.

P. Wilmott, Paul Wilmott Introduces Quantitative Finance, John Wiley and Sons, New York (2001).

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Published

2017-10-30
CITATION

How to Cite

Meena, S., & Vivin, J. V. (2017). Solution of Black-Scholes Equation on Barrier Option. Journal of Informatics and Mathematical Sciences, 9(3), 775–780. https://doi.org/10.26713/jims.v9i3.939

Issue

Vol. 9 No. 3 (2017)

Section

Research Articles

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