  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.
