Arbitrage Restrictions and Multi-Factor Models of the Term Structure of Interest Rates

In this paper we investigate models of the term structure where the factors are interest rates. As an example, we derive a no-arbitrage model of the term structure in which any two futures (as opposed to forward) rates act as factors. The term structure shifts and tilts as the factor rates vary. The cross-sectional properties of the model derive from the solution of a two-dimensional autoregressive process for the short rate, which exhibits mean reversion and a lagged memory parameter. We show that the correlation of the factor rates is restricted by the no-arbitrage conditions of the model. Hence in a multiple-factor model it is not valid to independently choose both the mean reversion, volatility and correlation parameters, contrary to the approach of some models in the literature. The term-structure model, derived here, can be used to value options on bonds and swaps or to generate term structure scenarios for the risk management of portfolios of interest-rate derivatives.