Comment: 53 pages, 18 figuresIn a globalised world, inflation in a given country may be becoming less responsive to domestic economic activity, while being increasingly determined by international conditions. Consequently, understanding the international sources of vulnerability of domestic inflation is turning fundamental for policy makers. In this paper, we propose the construction of Inflation-at-risk and Deflation-at-risk measures of vulnerability obtained using factor-augmented quantile regressions estimated with international factors extracted from a multi-level Dynamic Factor Model with overlapping blocks of inflations corresponding to economies grouped either in a given geographical region or according to their development level. The methodology is implemented to inflation observed monthly from 1999 to 2022 for over 115 countries. We conclude that, in a large number of developed countries, international factors are relevant to explain the right tail of the distribution of inflation, and, consequently, they are more relevant for the vulnerability related to high inflation than for average or low inflation. However, while inflation of developing low-income countries is hardly affected by international conditions, the results for middle-income countries are mixed. Finally, based on a rolling-window out-of-sample forecasting exercise, we show that the predictive power of international factors has increased in the most recent years of high inflation.