CALIBRATION OF CHAOTIC MODELS FOR INTEREST RATES

Abstract. 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. Key words. Positive interest rate models, Wiener chaos, model calibratio