The complexity of the forward interest rates, or forward rates, is far greater than that encountered in the study of stocks and their derivatives; the reason being that a stock at a given instant in time is described by only one degree of freedom that is undergoing random evolution, whereas in the case of the interest rates it is the entire yield curve that is randomly evolving and requires infinitely many degrees of freedom for its description. The theory of quantum fields has been developed precisely to study problems involving infinitely many (independent) degrees of freedom, and so one is naturally led to its techniques in the study of the interest yield curve.

The most widely used model of the forward rates is the HJM model. The fundamental limitation of the HJM model is that all the forward rates are exactly correlated, leading, for instance, to the unreasonable possibility of hedging a 30-year Treasury Bond with a six-month Treasury Bill. Models in which the forward rates have nontrivial correlation are more general, and it will be seen later from the empirical studies of the forward rates that such nontrivial correlations in fact exist in the financial markets.

Field theory models are able to incorporate correlation between forward rate maturities in a parsimonious manner that is well suited to analytical and computational studies as well as to empirical implementation. This is the main motivation for studying the forward interest rates from the point of view of quantum field theory.