General equilibrium pricing of CPI derivatives

We examine the issue of pricing forward futures and option contracts written on the Consumer Price Index (CPI), the change of which is a measure of inflation affecting the economy. Traditional approaches postulate an exogenous process for the price level and then derive CPI derivatives prices by standard arbitrage arguments. By contrast, we build the general equilibrium of a continuous time monetary economy that is affected by both real and nominal shocks. The price level and thus the inflation rate are found endogenously and solutions for the prices of CPI derivatives are obtained, which are in closed form in a specialized version of the economy.