Stochastic dividend discount model: covariance of random stock prices

  • Arianna AgostoEmail author
  • Alessandra Mainini
  • Enrico Moretto


The price of common stocks, defined as the sum of all future discounted dividends, is at the heart of both the dividend discount models (DDM) and the stochastic DDM (SDDM). Gordon and Shapiro (Manag Sci 3:102–110 1956) assume a deterministic and constant dividends’ growth rate, whereas Hurley and Johnson (Financ Anal J 4:50–54 1994, J Portf Manag 25(1)27–31 1998) and Yao (J Portf Manag 23(4)99–103 1997) introduce randomness by letting the growth rate be a finite-state random variable and random dividends behave in a Markovian fashion. In this second case expected stock price is determined, but what if higher-order moments are needed? In order to address a number of financial topics, the present contribution presents an explicit formula for the covariance between (possibly) correlated stock prices.


Stock valuation Dividend discount model Markov chain Financial risk management 

JEL Classification

G11 G12 G32 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Banca Carige SpAGenovaItaly
  2. 2.Dipartimento di Discipline matematiche, Finanza matematica ed EconometriaUniversitá Cattolica del Sacro CuoreMilanoItaly
  3. 3.Dipartimento di EconomiaUniversitá degli Studi dell’InsubriaVareseItaly
  4. 4.CNR-IMATIMilanoItaly

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