A simple finite-difference stock market model involving intrinsic value Jan Melecky ´ * , Artur Sergyeyev Mathematical Institute, Silesian University in Opava, Na Rybnı ´c ˇku 1, 74601 Opava, Czech Republic Accepted 2 January 2007 Abstract We suggest a deterministic delay difference model for the time series of the closing stock price and the intrinsic value of the stock. The most important new feature of this model is the equation describing the evolution of the intrinsic value. We present a general solution for the model in question and study the stability of the stationary points. Com- parison with the real-world data shows that upon a suitable choice of parameters our model exhibits a behavior rea- sonably similar to that of the real stock, at least for shorter time ranges (those of several weeks). Ó 2007 Elsevier Ltd. All rights reserved. 1. Introduction Nowadays there is a considerable interest in finding models describing the stock market behavior. The reasons for this interest are obvious: having such models at hand would considerably improve our understanding of the inner work- ings of the financial markets in general and could eventually lead to suggesting efficient strategies for the stock market participants. Our goal here is to suggest a simple finite-difference deterministic model for the time evolution of the stock price and the intrinsic value of the stock. The behavior of stock prices is often volatile and apparently chaotic, and most authors try to reproduce this behav- ior using either the stochastic approach or deterministic chaos in nonlinear systems, or a combination of these two, see e.g. recent papers [7,8,11,13,16] and references therein, as well as, for instance, the classical papers [21,23,25]. There is a considerable variance in specific approaches to the choice of dynamical variables and of the evolution parameter (continuous or discrete time), as well as in the intrinsic description of the inner workings of stock market. Discussing this here in detail is virtually impossible in view of the sheer number and volume of the papers on the subject, so we shall concentrate on the ideas and concepts pertinent to our model. The first important feature of our approach is to model the closing price time series (i.e., we consider the stock price P i at the end of ith business day) rather than the intraday ones (i.e., the time series for the stock price within a single business day). Proceeding in this way has two main advantages. First, the influence of random fluctuations of the stock price is considerably reduced. Second, as the time variable is now discrete, the resulting model is somewhat easier to analyze (cf. also [9]). This treatment of discrete time is different from the commonly used interpretation, cf. 0960-0779/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2007.01.016 * Corresponding author. E-mail addresses: Jan.Melecky@math.slu.cz (J. Melecky ´), Artur.Sergyeyev@math.slu.cz (A. Sergyeyev). Available online at www.sciencedirect.com Chaos, Solitons and Fractals 38 (2008) 769–777 www.elsevier.com/locate/chaos