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
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.