Forgive, or Award Your Debtor? A Barrier Option Approach

Abstract

Dealing with default risk on sovereign debt became an urgent matter with the Financial Crisis of 2008. Depending on both exogenous and endogenous factors, the risk of eventual default may become significant over the lifetime of a loan. Creditors are then faced with a dilemma, since they cannot force the borrowing country into bankruptcy court. Should they ease repayment by reducing the principal of the debt (“forgiveness”), or should they offer an extra award if the borrower repays in full? The latter award could come in the form of lower borrowing costs in the future. In this article, Sun and Chen propose to model the possibility of loan modification for risky sovereign debt as a kind of down-and-in put option: There is a boundary value (the “default threshold”) for the country’s perceived ability to pay, measured as the ratio of debt principal to GDP, at which the terms of the debt are revised, either to reduce the principal or to offer a repayment award. Both approaches have been tried in practice. What the authors show is that forgiveness is better for the creditors than a repayment award. The sensitivity of bond value to default boundary, forgiveness amount, and repayment award within the model are explored through simulation. The authors then conduct an empirical analysis on the bonds of 17 of the G20 countries to estimate the values of these three model parameters, and show that their model performs well in practice.