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Analytic solving of asset pricing models: The by force of habit case


  • Chen, Yu
  • Cosimano, Thomas F.
  • Himonas, Alex A.


Analytic methods for solving asset pricing models are developed to solve asset pricing models. Campbell and Cochrane's [1999. By force of habit, a consumption-based explanation of aggregate stock market behavior. Journal of Political Economy 107, 205-251] habit persistence model provides a prototypical example to illustrate this method. When the parameters involved satisfy certain conditions, the integral equation of this model has a solution in the space of continuous functions that grows exponentially at infinity. However, the parameters advocated by Campbell and Cochrane do not satisfy one of these conditions. The existence problem is removed by restricting the price-dividend function to avoid values of dividend growth that are extreme. Thus, existence and uniqueness of the solution in the space of continuous and bounded functions is proved. Using complex analysis the price-dividend function is also shown to be analytic in a region large enough to cover all relevant values of dividend growth. Next, a numerical method is presented for computing higher order polynomial approximations of the solution. Finally, a uniform upper bound on the error of these approximations is derived. An intensive search of the parameter space results in no parameter values for which the solution matches the historic equity premium and Sharpe ratio within Campbell and Cochrane's model.

Suggested Citation

  • Chen, Yu & Cosimano, Thomas F. & Himonas, Alex A., 2008. "Analytic solving of asset pricing models: The by force of habit case," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3631-3660, November.
  • Handle: RePEc:eee:dyncon:v:32:y:2008:i:11:p:3631-3660

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    References listed on IDEAS

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    Cited by:

    1. Cosimano, Thomas F., 2008. "Optimal experimentation and the perturbation method in the neighborhood of the augmented linear regulator problem," Journal of Economic Dynamics and Control, Elsevier, vol. 32(6), pages 1857-1894, June.
    2. Yu Chen & Thomas Cosimano & Alex Himonas, 2010. "Continuous time one-dimensional asset-pricing models with analytic price–dividend functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 461-503, March.
    3. Pohl, Walt, 2016. "External habit: Anything goes," Economics Letters, Elsevier, vol. 146(C), pages 140-142.
    4. Yu Chen & Thomas Cosimano & Alex Himonas & Peter Kelly, 2014. "An Analytic Approach for Stochastic Differential Utility for Endowment and Production Economies," Computational Economics, Springer;Society for Computational Economics, vol. 44(4), pages 397-443, December.

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