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A Generalized Endogenous Grid Method for Default Risk Models

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  • Youngsoo Jang
  • Soyoung Lee

Abstract

Default risk models have been widely employed to assess the ability of households and sovereigns to insure themselves against shocks. Grid search has often been used to solve these models because the complexity of the problem prevents the use of faster but less general methods. In this paper, we propose an extension of the endogenous grid method for default risk models, which is faster and more accurate than grid search. In particular, we find that our solution method leads to a more accurate bond price function, thus making substantial differences in the model’s main predictions. When applied to Arellano’s (2008) model, our approach predicts a standard deviation of the interest rate spread one-third lower and defaults 3 to 5 times less frequently than does the conventional approach. On top of that, our method is efficient. It is approximately 4 to 7 times faster than grid search when applied to a canonical model of Arellano (2008) and 19 to 27 times faster than grid search when applied to the richer model of Nakajima and Ríos-Rull (2014). Finally, we show that our method is applicable to a broad class of default risk models by characterizing sufficient conditions.

Suggested Citation

  • Youngsoo Jang & Soyoung Lee, 2021. "A Generalized Endogenous Grid Method for Default Risk Models," Staff Working Papers 21-11, Bank of Canada.
  • Handle: RePEc:bca:bocawp:21-11
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    References listed on IDEAS

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    1. Juan Carlos Hatchondo & Leonardo Martinez & César Sosa-Padilla, 2016. "Debt Dilution and Sovereign Default Risk," Journal of Political Economy, University of Chicago Press, vol. 124(5), pages 1383-1422.
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    5. Barillas, Francisco & Fernandez-Villaverde, Jesus, 2007. "A generalization of the endogenous grid method," Journal of Economic Dynamics and Control, Elsevier, vol. 31(8), pages 2698-2712, August.
    6. Carroll, Christopher D., 2006. "The method of endogenous gridpoints for solving dynamic stochastic optimization problems," Economics Letters, Elsevier, vol. 91(3), pages 312-320, June.
    7. Fedor Iskhakov & Thomas H. Jørgensen & John Rust & Bertel Schjerning, 2017. "The endogenous grid method for discrete‐continuous dynamic choice models with (or without) taste shocks," Quantitative Economics, Econometric Society, vol. 8(2), pages 317-365, July.
    8. Cristina Arellano, 2008. "Default Risk and Income Fluctuations in Emerging Economies," American Economic Review, American Economic Association, vol. 98(3), pages 690-712, June.
    9. Nakajima, Makoto, 2017. "Assessing bankruptcy reform in a model with temptation and equilibrium default," Journal of Public Economics, Elsevier, vol. 145(C), pages 42-64.
    10. Villemot, Sébastien, 2012. "Accelerating the resolution of sovereign debt models using an endogenous grid method," Dynare Working Papers 17, CEPREMAP.
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    More about this item

    Keywords

    Credit and credit aggregates; Credit risk management;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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