A Continuous-Time Model for Reinvestment Risk in Bond Markets

Abstract

When comparing standard bond market models with practice we observe that whereas the literature places no restrictions on the time to maturity of traded bonds this is actually the case in practice. Hence standard models ignore the reinvestment risk present in practice when considering contacts with longer time to maturity than the longest bond traded in the market. In this paper we propose a model including this reinvestment risk. We place a restriction on the bonds traded in the market by limiting the time \emph{to} maturity of traded bonds. At fixed times new bonds are issued in the market, thus extending the time of maturity of traded bonds. The initial prices of the new bonds issued in the market depend on the information generated by the market and a stochastic variable independent hereof describing the reinvestment risk. In order to quantify and control the reinvestment risk we apply the criterion of risk-minimization.