2011/06/13 by Matheus R. Grasselli, Grasselli, Matheus R, Tsunehiro Tsujimoto +1
Economics, Econometrics and Finance · #91G20 #91G30 #91G70 #Complex Systems and Time Series Analysis #FOS: Economics and business #Financial Risk and Volatility Modeling #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1106.2478
openalex publication_date 2011/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.