MELLIN TRANSFORM METHOD FOR THE VALUATION OF SOME VANILLA POWER OPTIONS WITH NON-DIVIDEND YIELD

Abstract

This paper presents the Mellin transform method for the val- uation 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. (15) 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 pro- vide a sufficient numerical analysis, we compare the results generated by the Mellin transform method for the valuation of American power put option for n = 1 which pays no dividend yield to two other numerical methods namely Crank Nicolson finite difference method (2) and binomial model (3) for options valuation against Black-Scholes analytical pricing formula (1). The numerical experiment shows that the Mellin transform method is efficient, easy to imple- ment, agree with the values of Black-Scholes (1), Crank Nicolson finite difference method (2) and binomial model (3). 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.