Inflation Securities Valuation with Macroeconomic-Based No-Arbitrage Dynamics

Abstract

We develop a model to price inflation and interest rates derivatives using continuous-time dynamics that have some links with macroeconomic monetary DSGE models equipped with a Taylor rule: in particular, the reaction function of the central bank, the bond market liquidity, inflation and growth expectations play an important role. The model can explain the effects of non-standard monetary policies (like quantitative easing or its tapering) and shed light on how central bank policy can affect the value of inflation and interest rates derivatives.The model is built under standard no-arbitrage assumptions. Interestingly, the model yields short rate dynamics that are consistent with a time-varying Hull-White model, therefore making the calibration to the nominal interest curve and options straightforward. Further, we obtain closed forms for both zero-coupon and year-on-year inflation swap and options. The calibration strategy we propose is fully separable, which means that the calibration can be carried out in subsequent simple steps that do not require heavy computation. A market calibration example is provided.The advantages of such structural inflation modelling become apparent when one starts doing risk analysis on an inflation derivatives book: because the model explicitly takes into account economic variables, a trader can easily assess the impact of a change in central bank policy on a complex book of fixed income instruments, which is normally not straightforward if one is using standard inflation pricing models.