We explore the interplay between sovereign debt default and climate risk. Pollution (e.g., pollution from land use, natural resource exploitation) contributes to the likelihood of natural disasters and influences economic growth rates. The country can default on its debt at any time while also deciding whether to invest in pollution abatement. The framework provides insights into the credit spreads of sovereign bonds and explains the observed relationship between bond spread and country's climate vulnerability. Through calibration for developing and low-income countries, we show that there is limited incentive for these countries to address climate risk, and the sensitivity of bond spreads to climate vulnerability is limited. Climate risk does not play a relevant role on the decision to default on sovereign debt. Financial support for climate abatement expenditures can effectively foster climate adaptation actions, instead renegotiation conditional upon pollution abatement does not produce any effect.