  In this paper we calibrate chaotic models for interest rates to market data
using a polynomial-exponential parametrization for the chaos coefficients. We
identify a subclass of one-variable models that allow us to introduce
complexity from higher order chaos in a controlled way while retaining
considerable analytic tractability. In particular we derive explicit
expressions for bond and option prices in a one-variable third chaos model in
terms of elementary combinations of normal density and cumulative distribution
functions. We then compare the calibration performance of chaos models with
that of well-known benchmark models. For term structure calibration we find
that chaos models are comparable to the Svensson model, with the advantage of
guaranteed positivity and consistency with a dynamic stochastic evolution of
interest rates. For calibration to option data, chaos models outperform the
Hull and White and rational lognormal models and are comparable to LIBOR market
models.
