Covariance of random stock prices in the Stochastic Dividend Discount Model

Dividend discount models have been developed in a deterministic setting. Some authors (Hurley and Johnson, 1994 and 1998; Yao, 1997) have introduced randomness in terms of stochastic growth rates, delivering closed-form expressions for the expected value of stock prices. This paper extends such previous results by determining a formula for the covariance between random stock prices when the dividends' rates of growth are correlated. The formula is eventually applied to real market data.