# A Quadratic Gaussian Year-on-year Inflation Model – University of Copenhagen

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# A Quadratic Gaussian Year-on-year Inflation Model

Specialeforsvar ved Peter Nørby Friis Sørensen

Titel: A Quadratic Gaussian Year-on-year Inflation Model

Abstract: We specify the Quadratic Gaussian Year-on-year inflation model (QGY), in which the year-on-year inflation ratio and the nominal bond are Markovian log-quadratic functions of multidimensional Gaussian processes. The year-on-year inflation ratio is defined on a strictly increasing tenor structure, making simulation of both the year-on-year ratio and inflation index easy. We demonstrate how to calculate the expectation of log-quadratic Gaussian processes and use this to derive a Black-Scholes like formula for the year-on-year inflation caplet in a semi-analytical form. We outline a method for numerical integration of a multivariate Gaussian density over a quadratic domain and use this in the semi-analytical form for the year-on-year inflation caplet. We specify a reduced and reparametrised version of the QGY model where the year-on-year inflation ratio is driven by two factors and where the payment delay convexity correction and the year-on-year convexity correction is easily adjusted. We calibrate this model to year-on-year inflation caps and floors on the eurozone's Harmonised Index of Consumer Prices Excluding Tobacco (HICPxT) and see that the model fits the year-on-year inflation volatility smile rather well. Finally, we use the calibrated QGY model to price HICPxT zero-coupon inflation caps and floors and compare the implied zero-coupon volatilities with market volatilities

Vejleder:  David G. Skovmand
Censor:    Bjarne Astrup Jensen, CBS