According to the macro-econometric literature, the impact of exogenous oil price shocks on Inflation have greatly increased in the last two decades throughout OECD countries while the persistence of those shocks on long-term inflation, namely core inflation, has dramatically decreased. In the meantime, the market for inflation derivatives soared, spurred by a revival of the primary inflation-linked bond market. As the contribution of core inflation to the total headline inflation volatility

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... omed, most of the volatility of headline inflation should thus be explained by changes in the spread between headline and core inflation indicators: a factor closely linked to commodity markets. This economic analysis should have important financial arbitrage implications in the futures market: are exogenous shocks on oil futures markets incorporated into zero coupon inflation indexed swap prices? To investigate this issue, we propose on the one hand a four-factor model for both inflation and nominal rates, and on the other hand a two-factor model for commodities. We proceed to an empirical estimation of the model using prices of oil futures contracts and inflation breakeven rates from which we can in particular extract a synthetic core inflation forward curve.