TABLE OF CONTENTS This article elaborates an n-order multinomial lattice approach to value derivative instruments on asset prices characterized by a lognormal distribution. Nonlinear optimization is employed, specified moments are matched, and n-order multinomial trees are developed. The proposed methodology represents an alternative specification to models of jump processes of order greater than three developed by other researchers. The main contribution of this work is pedagogical. Its strength is in its straightforward explanation of the underlying tree building procedure for which numerical efficiency is a motivation for actual implementation.
Keywords: Lattice; multinomial; derivatives; moment matching; numerical efficiency.
Since the seminal article by Black and Scholes (BS, 1973), numerous methods for valuing derivative securities have been proposed. Merton (1973) extended the BS model to include valuing an option on a stock or index that pays continuous dividends. From this framework, the BS model was easily extended to currency options. In the case of exotic contracts where there is no closed form solution, various techniques have been elaborated including Monte-Carlo simulation, numerical integration, analytical and series approximation, jump processes, and finite difference methods. Parkinson (1977) applied a three-jump model via numerical integration...
