Pricing and hedging of inflation-indexed bonds in an affine framework

摘要

This study deals with the pricing and hedging of inflation-indexed bonds. Under foreign exchange analogy we model the nominal short rate, real short rate and logarithm of the price index with an affine Gaussian process. Using the underlying affine property, we compute the nominal and inflation-indexed bond prices explicitly. We derive no-arbitrage drift conditions for the factor process. Then, we perform a novel hedging analysis where our objective is to replicate an indexed bond of a given maturity by trading a portfolio of nominal bonds. This analysis leads to a hedging criterion based on a set of restrictions on the eigenvalues and the eigenvectors of mean reversion speed matrix of the factor process. We fit the model to the US bond data and perform an in-sample hedging analysis. Having relatively small in-sample hedging errors, we validate the theoretical hedging result for the considered dataset.