We consider a continuous-time framework featuring a central bank, private agents, and a financial market. The central bank's objective is to maximize a functional, which measures the classical trade-off between output and inflation over time plus income from the sales of inflation-indexed bonds minus payments for the liabilities that the inflation-indexed bonds produce at maturity. Private agents are assumed to have adaptive expectations. The financial market is modeled in continuous-time BlackScholes-Merton style and financial agents are averse against inflation risk, attaching an inflation risk premium to nominal bonds. Following this route, we explain demand for inflation-indexed securities on the financial market from a no-arbitrage assumption and derive pricing formulas for inflation-linked bonds and calls, which lead to a supply-demand equilibrium. Furthermore, we study the consequences that the sales of inflation-indexed securities have on the observed inflation rate and price level. Similar to the study of Walsh, we find that the inflationary bias is significantly reduced, and hence that markets for inflation-indexed bonds provide a mechanism to reduce inflationary bias and increase central bank's credibility.
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 a mechanism to implement inflation contracts as discussed in the classical literature.
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