A semi-Markov approach to the stock valuation problem

In this paper, a general model is provided to evaluate a stock when the dividend growth rate is a discrete variable. This new dividend valuation model assumes that the dividend growth rate follows a finite state discrete time semi-Markov chain. An important consequence is that prices become duration dependent, i.e. they are influenced not only by the current state of the dividend growth process but also by the elapsed time in this state. This general valuation setting necessitates a more complex solution procedure with respect to the Markovian models. In fact, the valuation procedure of the semi-Markov model requires the solution of a system of first order linear difference equations with variable coefficients. The model is implemented by using experimental data freely available at <ExternalRef> <RefSource>http://www.econ.yale.edu/shiller/data.htm</RefSource> <RefTarget Address="http://www.econ.yale.edu/shiller/data.htm" TargetType="URL"/> </ExternalRef>. The parameters of the model are estimated and the data strongly support the semi-Markov hypothesis of the dividend growth rate process. The paper generalizes previous contributions dealing with pricing firms on the basis of fundamentals. Copyright Springer-Verlag 2013