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 bottomed, 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.
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