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IJSTR >> Volume 3- Issue 12, December 2014 Edition



International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616



Black-Scholes Partial Differential Equation In The Mellin Transform Domain

[Full Text]

 

AUTHOR(S)

Fadugba Sunday Emmanuel, Ogunrinde Roseline Bosede

 

KEYWORDS

Keywords: Black-Scholes Model, Black-Scholes Partial Differential Equation, Dividend Yield, European Option, Mellin Transform Method, Option

 

ABSTRACT

Abstract: This paper presents Black-Scholes partial differential equation in the Mellin transform domain. The Mellin transform method is one of the most popular methods for solving diffusion equations in many areas of science and technology. This method is a powerful tool used in the valuation of options. We extend the Mellin transform method proposed by Panini and Srivastav [7] to derive the price of European power put options with dividend yield. We also derive the fundamental valuation formula known as the Black-Scholes model using the convolution property of the Mellin transform method. 2010 Mathematics Subject Classification: 44A15, 60H30, 91G99

 

REFERENCES

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[2] Erdelyi A, et al. (1954), Tables of Integral Transforms, Vol. 1-2, First Edition, McGraw-Hill, New York.

[3] Fadugba S. E. and C. R. Nwozo (2014), On the Comparative Study of Some Numerical Methods for Vanilla Option Valuation, Communication in Applied Sciences, Vol. 2, No. 1.

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[5] Nwozo C.R. and Fadugba S.E. (2012), Monte Carlo Method for Pricing Some Path Dependent Options, International Journal of Applied Mathematics, Vol. 25, No. 6, 763-778.

[6] Panini R. and Srivastav R.P. (2004), Pricing Perpetual Options using Mellin Transforms, Applied Mathematics Letters, Vol. 18, 471-474, doi: 10.1016/j.aml.2004.03.012.

[7] Panini R. and Srivastav R.P. (2004), Option Pricing with Mellin Transforms, Mathematical and Computer Modelling, Vol. 40, 43-56, doi:10.1016/j.mcm.2004.07.008.

[8] Vasilieva O. (2009), A New Method of Pricing Multi-Options using Mellin Transforms and Integral Equations, Master's Thesis in Financial Mathematics, School of Information Science, Computer and Electrical Engineering, Halmsta University.

[9] Yakubovich S.B. and Nguyen T.H. (1991), The Double Mellin-Barnes Type Integrals and their Applications to Convolution Theory, Series on Soviet Mathematics, World Scientific, 199.

[10] Zieneb A.E. and Rokiah R.A. (2011), Analytical Solution for an Arithmetic Asian Option using Mellin Transforms, Vol. 5, 1259-1265.