2014/03/30 by Gabriele Sarais, Sarais, Gabriele, Damiano Brigo +1
Economics, Econometrics and Finance · #Economic theories and models #Stochastic processes and financial applications #Monetary Policy and Economic Impact
paper · pdf · doi:10.48550/arxiv.1403.7799
We develop a model to price inflation and interest rates derivatives using\ncontinuous-time dynamics that have some links with macroeconomic monetary DSGE\nmodels equipped with a Taylor rule: in particular, the reaction function of the\ncentral bank, the bond market liquidity, inflation and growth expectations play\nan important role. The model can explain the effects of non-standard monetary\npolicies (like quantitative easing or its tapering) and shed light on how\ncentral bank policy can affect the value of inflation and interest rates\nderivatives.\n The model is built under standard no-arbitrage assumptions. Interestingly,\nthe model yields short rate dynamics that are consistent with a time-varying\nHull-White model, therefore making the calibration to the nominal interest\ncurve and options straightforward. Further, we obtain closed forms for both\nzero-coupon and year-on-year inflation swap and options. The calibration\nstrategy we propose is fully separable, which means that the calibration can be\ncarried out in subsequent simple steps that do not require heavy computation. A\nmarket calibration example is provided.\n The advantages of such structural inflation modelling become apparent when\none starts doing risk analysis on an inflation derivatives book: because the\nmodel explicitly takes into account economic variables, a trader can easily\nassess the impact of a change in central bank policy on a complex book of fixed\nincome instruments, which is normally not straightforward if one is using\nstandard inflation pricing models.\n