Optimal Contracts for Central Bankers : Calls on Inflation

We consider a framework featuring a central bank, private and financial agents as well as a financial market. The central bank's objective is to maximize a functional, which measures the classical trade-off between output and inflation plus income from the sales of inflation linked calls minus payments for the liabilities that the inflation linked calls produce at maturity. Private agents have rational expectations and financial agents are averse against inflation risk. Following this route, we explain demand for inflation linked calls on the financial market from a no-arbitrage assumption and derive pricing formulas for inflation linked calls, which lead to a supply-demand equilibrium. We then study the consequences that the sales of inflation linked calls have on the observed inflation rate and price level. Similar as in Walsh (1995) we find that the inflationary bias is significantly reduced, and hence that markets for inflation linked calls provide provide a mechanism to implement inflation contracts as discussed in the classical literature