Pricing inflation derivatives

Objectives: We develop a model of nominal yields and inflation that is used to value various types of inflation derivatives. It also allows us to derive estimates of expected inflation, accounting for both the inflation risk premium and the distortion due to the zero lower bound on nominal rates. Accurate pricing of inflation derivatives will also enable us to  back out a (risk-neutral) probability distribution for inflation.

Data/Methods: Our nominal term structure model is a no-arbitrage Gaussian 3-factor model that imposes a zero lower bound on interest and forward rates. The zero lower bound creates a non-linearity that makes traditional recursive solution techniques infeasible, and we employ a second-order approximation to a shadow-rate model to  obtain a solution. Its parameters are estimated by a Maximum Llikelhood/Kalman filter technique using data on U.S. Treasury yields (and survey forecasts of the yields on the 3-month Treasury bill and the 10-year Treasury note). We also propose a two-factor Gaussian model of inflation with Poisson jumps, where the frequency of jumps follows a Hawkes process. This inflation model is estimated using data on zero-coupon interest rate swaps, caps, and floors, as well as survey forecasts of inflation. We first estimate the inflation model assuming inflation has zero correlation with nominal interest rates and that jump frequencies are constant.

Results/Expected Results: These assumptions allow us to obtain analytic solutions. We then show the importance of loosening the zero-correlations assumption and permitting time-varying jump frequencies by estimating the model parameters using Monte Carlo simulation of the values of inflation swaps, caps, floors, and survey forecasts of inflation.