Indexed Bonds With Mean-Reverting Risk Factors

Abstract

In this paper, we focus on the value of inflation-indexed bonds in an extended short rate model, which is a specific case of the general framework provided by Jarrow and Yildirim (2003). In the model, we assume mean-reverting stochastic dynamics under the risk neutral measure for both the short interest rate and the instantaneous inflation rate. We define the zero-coupon inflation-indexed bond, and first estimate its value by Monte Carlo simulation, then deduce an analytical formula as well. We briefly touch on the yield and inflation curves the model is able to produce.