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.

Highlights

  • The derivative market has becomes extremely popular, this popularity even exceeds that of the stock exchange

  • We have considered the Mellin transform method for the valuation of some vanilla power options

  • We have established a formula for the valuation of European power put option using the Mellin transform method on a non-dividend yield consisting of single integral

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Summary

Introduction

The derivative market has becomes extremely popular, this popularity even exceeds that of the stock exchange. [16] derived a closed-form expression for the free boundary and price of a perpetual American put option using Mellin transform techniques, Frontczak F. and Schobel [8] extended a framework based on the Mellin transforms and showed how to modify the approach to value American call options on dividend paying stocks, Zieneb A.E and Rokiah R.A [21] derived a closed form solution for a continuous arithmetic Asian option by means of partial differential equation. They provided a new method for solving arithmetic Asian options using Mellin transforms in a stock price.

Power Options
A Review of Classic Integral Transforms
The Mellin Transform Method
Some Integral Representations for European Power Call and Put Options Payoffs
Numerical Experiment
Example
Discussion of Results
Conclusion
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