IJPAM: Volume 96, No. 1 (2014)
OF SOME VANILLA POWER OPTIONS
WITH NON-DIVIDEND YIELD
Department of Mathematics
University of Ibadan
Oyo State, NIGERIA
Department of Mathematical Sciences
Ekiti State University
Ado Ekiti, NIGERIA
Abstract. This paper presents the Mellin transform method for the valuation of some vanilla power options with non-dividend yield. This method is a powerful tool used in the valuation of options. We extend the Mellin transform method proposed by Panini R. and Srivastav R.P.  to derive the price of European and American power put options with non-dividend yield. We also derive the fundamental valuation formula known as the Black-Scholes model using the convolution property of the Mellin transform method. To provide a sufficient numerical analysis, we compare the results generated by the Mellin transform method for the valuation of American power put option for which pays no dividend yield to two other numerical methods namely Crank Nicolson finite difference method  and binomial model  for options valuation against Black-Scholes analytical pricing formula . The numerical experiment shows that the Mellin transform method is efficient, easy to implement, agree with the values of Black-Scholes , Crank Nicolson finite difference method  and binomial model . Hence the Mellin transform method is a better alternative method compared to the Crank Nicolsion finite difference and binomial model for the valuation of some vanilla power options.
Received: June 2, 2014
AMS Subject Classification: 44A15, 44A99, 60H30, 91G20, 91G99
Key Words and Phrases: American option, European power option, Mellin transform method, non-dividend yield
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DOI: 10.12732/ijpam.v96i1.7 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 79 - 104