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Calibration of Chaotic Models for Interest Rates

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  • Matheus R Grasselli
  • Tsunehiro Tsujimoto
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    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.

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    File URL: http://arxiv.org/pdf/1106.2478
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1106.2478.

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    Date of creation: Jun 2011
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    Handle: RePEc:arx:papers:1106.2478

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    Web page: http://arxiv.org/

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    1. Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc.
    2. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348.
    3. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    4. repec:aah:aarmng:1999-4 is not listed on IDEAS
    5. L. C. G. Rogers, 1997. "The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 157-176.
    6. Feng Zhao & Robert Jarrow & Haitao Li, 2004. "Interest Rate Caps Smile Too! But Can the LIBOR Market Models Capture It?," Econometric Society 2004 North American Winter Meetings 431, Econometric Society.
    7. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
    8. Tino Kluge & L. C. G. Rogers, 2012. "The potential approach in practice," Papers 1204.5718, arXiv.org.
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