The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate. This paper develops an analytical framework that helps to quantify the optimal level of international reserves for a small open economy with limited access to foreign capital and subject to natural disasters or terms of trade shocks. International reserves allow the country to relieve balance of payments pressures caused by external shocks and to avoid large fluctuations in imports. I calibrate the model to two regions, the Caribbean and the Sahel, and assess the sensitivity of the results.