  The Wiener chaos approach to interest rate modelling arises from the
observation that the pricing kernel admits a representation in terms of the
conditional variance of a square-integrable random variable, which in turn
admits a chaos expansion. When the expansion coefficients factorise into
multiple copies of a single function, then the resulting interest rate model is
called coherent, whereas a generic interest rate model will necessarily be
incoherent. Coherent representations are nevertheless of fundamental importance
because incoherent ones can always be expressed as a linear superposition of
coherent elements. This property is exploited to derive general expressions for
the pricing kernel and the associated bond price and short rate processes in
the case of an n-th order chaos model for each $n$. The pricing formulae for
bond options and swaptions are obtained in closed forms for a number of
examples. An explicit representation for the pricing kernel of a
generic---incoherent---model is then obtained by use of the underlying coherent
elements. Finally, finite-dimensional realisations of the coherent chaos models
are investigated in detail. In particular, it is shown that a class of highly
tractable models can be constructed having the characteristic feature that the
discount bond price is given by a piecewise flat (simple) process.
