Integral Representations for the Price of Vanilla Put Options on a Basket of Two-Dividend Paying Stocks

This paper presents integral representations for the price of vanilla put options, namely, European and American put options on a basket of two-dividend paying stocks using integral method based on the double Mellin transform. We show that by the decomposition of the integral equation for the price of American basket put option, the integral equation for the price of European basket put option can be obtained directly.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Fadugba, S. and Nwozo, C. (2015) Integral Representations for the Price of Vanilla Put Options on a Basket of Two-Dividend Paying Stocks. Applied Mathematics, 6, 783-792. doi: 10.4236/am.2015.65074.

 [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.C. (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] Manuge, D.J. and Kim, P.T. (2015) Basket Option Pricing Using Mellin Transforms. Mathematical Finance Letter, 1, 1-9. [5] AlAzemi, F., AlAzemi, A. and Boyadjiev, I. (2014) Mellin Transform Method for Solving the Black-Scholes Equation. International Journal of Pure and Applied Mathematics, 97, 287-301. http://dx.doi.org/10.12732/ijpam.v97i3.3 [6] Boyle, P.P., Evnine, J. and Gibbs, S. (1989) Numerical Evaluation of Multivariate Contingent Claims. Review of Financial Studies, 2, 241-250. http://dx.doi.org/10.1093/rfs/2.2.241 [7] 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. http://dx.doi.org/10.11648/j.acm.s.20140301.11 [8] Frontczak, R. and Scho ?bel, R. (2009) On Modified Mellin Transforms, Gauss-Laguerre Quadrature and the Valuation of American Call Options. Working Paper, Tubinger Diskussionsbeitrag, No. 320. [9] Huynh, C.B. (1994) Back to Baskets. Risk, 5, 59-61. [10] Sneddon, I.N. (1972) The Use of Integral Transforms. McGraw-Hill, New York. [11] Turnbull, S.M. and Wakeman, L.M. (1991) A Quick Algorithm for Pricing European Average Options. The Journal of Financial and Quantitative Analysis, 26, 377-389. http://dx.doi.org/10.2307/2331213 [12] 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