In a fully micro-founded New Keynesian framework, we characterize an analytical relationship between average inflation and oil price volatility by solving the rational expectations equilibrium of the model up to second order of accuracy. The model shows that higher oil price volatility induces higher levels of average inflation. We also show that when oil has low substitutability in the production function, the higher the weight the central bank assigns to inflation in the policy rule, the lower the level of average inflation is. The analytical solution further indicates that, for a given level of oil price volatility, average inflation is higher when marginal costs are convex in oil prices, the Phillips Curve is convex, and the degree of relative price dispersion is higher. The evolution of inflation during the 70s and 80s is consistent with the prediction of the model.