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Real Options using Markov Chains: an application to Production Capacity Decisions


  • Dalila B. M. M. Fontes

    () (LIAAD and Faculdade de Economia da Universidade do Porto, Portugal)

  • Luís Camões

    () (Banif -- Banco Internacional do Funchal)

  • Fernando A. C. C. Fontes

    () (Departamento de Matemática para a Ciência e Tecnologia, Universidade do Minho)


In this work we address investment decisions using real options. A standard numerical approach for valuing real options is dynamic programming. The basic idea is to establish a discrete-valued lattice of possible future values of the underlying stochastic variable (demand in our case). For most approaches in the literature, the stochastic variable is assumed normally distributed and then approximated by a binomial distribution, resulting in a binomial lattice. In this work, we investigate the use of a sparse Markov chain to model such variable. The Markov approach is expected to perform better since it does not assume any type of distribution for the demand variation, the probability of a variation on the demand value is dependent on the current demand value and thus, no longer constant, and it generalizes the binomial lattice since the latter can be modelled as a Markov chain. We developed a stochastic dynamic programming model that has been implemented both on binomial and Markov models. A numerical example of a production capacity choice problem has been solved and the results obtained show that the investment decisions are different and, as expected the Markov chain approach leads to a better investment policy.

Suggested Citation

  • Dalila B. M. M. Fontes & Luís Camões & Fernando A. C. C. Fontes, 2007. "Real Options using Markov Chains: an application to Production Capacity Decisions," FEP Working Papers 246, Universidade do Porto, Faculdade de Economia do Porto.
  • Handle: RePEc:por:fepwps:246

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    References listed on IDEAS

    1. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
    2. Majd, Saman & Pindyck, Robert S., 1987. "Time to build, option value, and investment decisions," Journal of Financial Economics, Elsevier, vol. 18(1), pages 7-27, March.
    3. Pindyck, Robert S, 1988. "Irreversible Investment, Capacity Choice, and the Value of the Firm," American Economic Review, American Economic Association, vol. 78(5), pages 969-985, December.
    4. Kandel, Eugene & Pearson, Neil D., 2002. "Option Value, Uncertainty, and the Investment Decision," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(03), pages 341-374, September.
    5. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 707-727.
    6. He, Hua & Pindyck, Robert S., 1992. "Investments in flexible production capacity," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 575-599.
    7. Triantis, Alexander J & Hodder, James E, 1990. " Valuing Flexibility as a Complex Option," Journal of Finance, American Finance Association, vol. 45(2), pages 549-565, June.
    8. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    9. McDonald, Robert L & Siegel, Daniel R, 1985. "Investment and the Valuation of Firms When There Is an Option to Shut Down," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 331-349, June.
    10. Myers, Stewart C., 1977. "Determinants of corporate borrowing," Journal of Financial Economics, Elsevier, vol. 5(2), pages 147-175, November.
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    More about this item


    Flexible Capacity Investments; Real Options; Markov Chains; Dynamic Programming;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

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