Alternative Approach for the Solution of the Black-Scholes Partial Differential Equation for European Call Option
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Abstract: 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.
Cite this paper: Fadugba, S. and Ajayi, A. (2015) Alternative Approach for the Solution of the Black-Scholes Partial Differential Equation for European Call Option. Open Access Library Journal, 2, 1-8. doi: 10.4236/oalib.1101466.
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

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

[4]   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 Schöbel, R. (2009) On Modified Mellin Transforms, Gauss-Laguerre Quadrature and the Valuation of American Call Options. Tübinger Diskussionsbeitrag, No. 320.

[14]   Apostol, T.M. (1957) Mathematical Analysis. Addison Wesley, Reading.

[15]   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.

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