Parameter ranking of stock market dynamics: a comparative study of the mathematical models of competition and mutualistic interactions

Abstract

In this paper, we study a parameter ranking of stock market dynamics for two types of complex interactions in the context of stock markets over a trading period using a Lotka-Volterra system of non-linear first order ordinary differential equations. We started this study by describing the model under consideration and pointing out a few of the complexities inherent in our proposed model. Using the existing literature, we selected a set of best-fit model parameters and initial conditions which form the basis for our parameter ranking. Our parameter ranking or sensitivity analysis permits us to make realistic conclusions about the relative importance of individual parameters. Our approach also permits us to gain some useful insights into the ability of the model to reflect what is obtainable within the stock markets.

Keywords: Sensitivity analysis, competition interaction, mutualistic interaction