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A multivariate Markov chain stock model

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  • Guglielmo D'Amico
  • Riccardo De Blasis

Abstract

We propose a dividend stock valuation model where multiple dividend growth series and their dependencies are modelled using a multivariate Markov chain. Our model advances existing Markov chain stock models. First, we determine assumptions that guarantee the finiteness of the price and risk as well as the fulfilment of transversality conditions. Then, we compute the first- and second-order price-dividend ratios by solving corresponding linear systems of equations and show that a different price-dividend ratio is attached to each combination of states of the dividend growth process of each stock. Subsequently, we provide a formula for the computation of the variances and covariances between stocks in a portfolio. Finally, we apply the theoretical model to the dividend series of three US stocks and perform comparisons with existing models. The results could also be applied for actuarial purposes as a general stochastic investment model and for calculating the initial endowment to fund a portfolio of dependent perpetuities.

Suggested Citation

  • Guglielmo D'Amico & Riccardo De Blasis, 2020. "A multivariate Markov chain stock model," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(4), pages 272-291, April.
    • Handle: RePEc:taf:sactxx:v:2020:y:2020:i:4:p:272-291
    DOI: 10.1080/03461238.2019.1661280
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    Cited by:

    1. Battulga Gankhuu, 2023. "Parameter Estimation Methods of Required Rate of Return," Papers 2305.19708, arXiv.org, revised Aug 2023.
    2. D’Amico, Guglielmo & De Blasis, Riccardo & Petroni, Filippo, 2023. "The Mixture Transition Distribution approach to networks: Evidence from stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    3. D'Amico, Guglielmo & De Blasis, Riccardo, 2024. "Dividend based risk measures: A Markov chain approach," Applied Mathematics and Computation, Elsevier, vol. 471(C).

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