MODELING RANDOM ASSET RETURN BEHAVIOR USING AN OPTIMAL MULTI-PERIOD SPECTRUM

Abstract

Options have become extremely popular and the reasons behind that can be summarized in two points; they are attractive tools both for speculation and hedging. If their price can be determined: therefore their trading can be done with a certain confidence.The vendor of the option have two mains questions. How much should the buyer of the option pay in other words, how to access the price at the time t = 0 and the richness available at time T ?becomes the pricing problem. Multi fractals offer a well-defined set of answers to this question because it has the capability of generating various degree of long term memory in different powers of return. A model cannot capture all aspects of reality but rather a simple version that focuses on some particular point of interest. We present a dynamic multi-period spectrum model of variation of the capital market price aimed at determining the growth rate of an asset, using a continuous rate of return,???????? = −????−????????; and the optimal trading strategy.