## Quantitative properties of sovereign default models: solution methods matter

_IMF Working Papers, April 1, 2010_

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## Bibliographic details
- Authors: Leonardo Martinez, Horacio Sapriza, Juan Carlos Hatchondo
- Published: April 1, 2010
- Series: IMF Working Papers
- DOI: https://doi.org/10.5089/9781451982770.001

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### Summary
- Authors: Leonardo Martinez, Horacio Sapriza, Juan Carlos Hatchondo
- Date: April 1, 2010
- Core claim: The commonly used discrete state space technique with evenly spaced grid points in sovereign default models can generate spurious interest rate movements unless a large number of grid points is used; alternative approximation methods (Chebyshev polynomials or cubic spline interpolation) are significantly more efficient.

### Main findings
- Discrete state space technique with evenly spaced grid points:
  - Necessitates a large number of grid points to avoid generating spurious interest rate movements.
  - Is significantly more inefficient than using Chebyshev polynomials or cubic spline interpolation to approximate the value functions.
- Inefficiency is more severe for parameterizations that:
  - Feature a high sensitivity of the bond price to the borrowing level for the borrowing levels that are observed more frequently in the simulations.
- Efficiency of the discrete state space technique can be greatly improved by:
  - (i) Finding the equilibrium as the limit of the equilibrium of the finite-horizon version of the model, instead of iterating separately on the value and bond price functions.
  - (ii) Concentrating grid points in asset levels at which the bond price is more sensitive to the borrowing level and in levels that are observed more often in the model simulations.

### Methodological implications
- Interpolation/approximation choices materially affect quantitative properties of sovereign default models, including the cyclical behavior of interest rates in emerging market economies.
- Results in the sovereign default literature that rely on discrete state space methods with evenly spaced grids may lack robustness unless numerical resolution and grid placement issues are addressed.
- The analysis is relevant beyond sovereign default models to the study of other credit markets where bond price sensitivity and state-space discretization matter.

### Policy and research recommendations
- Researchers should evaluate alternative approximation methods (Chebyshev polynomials, cubic spline interpolation) when solving sovereign default models to improve computational efficiency and avoid spurious results.
- When using discrete state space techniques:
  - Consider computing equilibrium as the limit of finite-horizon equilibria rather than separate iterations on value and bond price functions.
  - Concentrate grid points in asset regions with higher bond price sensitivity and in regions more frequently visited in simulations to reduce inefficiency and bias.
- Reassess empirical and quantitative results from prior studies that used coarse or evenly spaced discrete grids without these improvements.

*IMF Working Papers — "Quantitative properties of sovereign default models: solution methods matter", Leonardo Martinez, Horacio Sapriza, Juan Carlos Hatchondo, April 1, 2010.*

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_Source: https://www.imf.org/en/publications/wp/issues/2016/12/31/quantitative-properties-of-sovereign-default-models-solution-methods-matter-23766_