In this paper we present an alternative approach for the solution of the
Black-Scholes partial differential equation for European call option which pays
dividend yield using the modified Mellin transform method. The approach used in
this paper does not require variables transformation. We also extend the
modified Mellin transform method for the valuation of European call option
which pays dividend yield. The numerical results show that the modified Mellin
transform is accurate, mutually consistent and agrees with the values of the
Black-Scholes model.
References
[1]
Black, F. and
Scholes, M. (1973) The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81,
637-654. http://dx.doi.org/10.1086/260062
[2]
Merton, R. (1973) Theory of Rational Option Pricing. Bell Journal of Economics and Management
Science, 4, 141- 183. http://dx.doi.org/10.2307/3003143
Nwozo, C.R.
and Fadugba,
S.E. (2014) Mellin
Transform Method for the Valuation of Some Vanilla Power Options with Non-Dividend
Yield. International Journal of Pure and Applied
Mathematics, 96, 79-104. http://dx.doi.org/10.12732/ijpam.v96i1.7
[5]
Jódar, L., Sevilla,
P., Cortes,
J.C. and Sala, R. (2005) A New Direct Method for Solving the
Black-Scholes Equation. Applied
Mathematics and Letters, 18, 29-32. http://dx.doi.org/10.1016/j.aml.2002.12.016
[6]
Al Azemi,
F., Al Azemi, A.
and Boyadjiev, I. (2014) Mellin Transform Method for Solving the
Black-Scholes Equation. International
Journal of Pure and Applied Mathematics, 97, 287-301.
[7]
Nwozo, C.R. and Fadugba, S.E. (2015) On Two Transform Methods for the Valuation of Contingent
Claims. Journal of Mathematical Finance,
5, 88-112. http://dx.doi.org/10.4236/jmf.2015.52009
[8]
Nwozo, C.R. and Fadugba, S.E. (2015) On Stochastic Volatility in the Valuation of European
Options. British
Journal of Mathematics and Computer Science, 5, 104-127. http://dx.doi.org/10.9734/BJMCS/2015/13176
[9]
Nwozo, C.R. and Fadugba, S.E. (2014) Performance
Measure of Laplace Transforms for Pricing Path Dependent Options. International Journal of Pure and Applied
Mathematics, 94, 175-197. http://dx.doi.org/10.12732/ijpam.v94i2.5
[10]
Fadugba, S.E. (2014) The Mellin Transforms Method as an Alternative
Analytic Solution for the Valuation of Geometric Asian Option. Applied and Computational Mathematics, Special Issue: Computational Finance, 3, 1-7.
[11]
Wilmott, P., Howison, S. and Dewynne, J. (1993) Option
Pricing: Mathematical Models and Computation. Oxford Financial Press, Oxford.
[12]
Wilmott, P., Howison, S. and Dewynne, J. (1997) The
Mathematics of Financial Derivatives. Cambridge University Press, Cambridge.
[13]
Frontczak, R. and Schobel, R. (2009) On Modified Mellin Transforms, Gauss-Laguerre Quadrature
and the Valuation of American Call Options. Tübinger Diskussionsbeitrag, No. 320.
Nwozo, C.R. and Fadugba, S.E. (2014) On
the Accuracy of Binomial Model for the Valuation of Standard Options with Dividend
Yield in the Context of Black-Scholes Model. IAENG
International Journal of Applied Mathematics, 44, 33-44.
