Implementing No-Arbitrage Term Structure of Interest Rate Models in Discrete Time When Interest Rates Are Normally Distributed

Abstract

The article develops a method for implementing nonarbitrage term structure of interest rate models for the single-factor model under the Heath-Jarrow-Morton (HJM) framework of the evolution of forward interest rates. The HJM framework is universal in the sense that it is based on the no-arbitrage condition, and it can accommodate nearly all existing models if interest rates - spot rate and forward rates - distributed normally. The implementation requires the calculation of drift adjustment terms (DATs) that are the functions of the volatility9s of forward rates. The method is equally effective with volatility functions that are integrable and those that are not. It is easy to understand, simple enough to implement for even difficult volatility functions, generalizable, and able to accommodate Monte Carlo simulations of interest rate modeling.