A stochastic Gordon-Shapiro formula with excess volatility

It is well-known that stock prices fluctuate far more than dividends. Traditional valuation methods are not able to depict this fact. In this paper we incorporate excess volatility into a simple DCF model by considering an autoregressive cash flows process with random coefficients. We show that the model is free of arbitrage and that the transversality condition is met and we prove a valuation equation that differs from the classical Gordon-Shapiro version: Cost of capital (respectively dividend-price ratio) is stochastic and our model represents excess volatility. We discuss whether our assumptions are compatible with an equilibrium.