A Continuous-Time Model of Sovereign Debt

I construct a continuous-time model of strategic default and provide a numerical algorithm that solves it. I compare the results and computation times to standard discrete-time models of sovereign debt. The method proposed here is faster than discrete-time computation methods while obtaining similar quantitative results. The few differences between the models can all be attributed to a painful deleveraging feature. When debt issuance happens at a higher frequency, the sovereign faces higher interest rate spreads along the deleveraging process. So rolling over its debt becomes more costly. This feature leads to a coefficient of variation for interest rate spreads that is higher and closer to the data relative to its discrete-time sovereign debt model counterpart, calibrated to quarterly frequency. I solve three variants of the model. The first includes short-term maturity bonds only and a constant risk-free interest rate. The second allows for stochastic fluctuations in the risk-free rate. Finally, I extend the model to allow for long-term bonds.