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Forecasting the Term Structure of Variance Swaps

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  • Kai Detlefsen
  • Wolfgang Härdle

Abstract

Recently, Diebold and Li (2003) obtained good forecasting results for yield curves in a reparametrized Nelson-Siegel framework. We analyze similar modeling approaches for price curves of variance swaps that serve nowadays as hedging instruments for options on realized variance. We consider the popular Heston model, reparametrize its variance swap price formula and model the entire variance swap curves by two exponential factors whose loadings evolve dynamically on a weekly basis. Generalizing this approach we consider a reparametrization of the three-dimensional Nelson-Siegel factor model. We show that these factors can be interpreted as level, slope and curvature and how they can be estimated directly from characteristic points of the curves. Moreover, we analyze a semiparametric factor model. Estimating autoregressive models for the factor loadings we get termstructure forecasts that we compare in addition to the random walk and the static Heston model that is often used in industry. In contrast to the results of Diebold and Li (2003) on yield curves, no model produces better forecasts of variance swap curves than the random walk but forecasting the Heston model improves the popular static Heston model. Moreover, the Heston model is better than the flexible semiparametric approach that outperforms the Nelson-Siegel model.

Suggested Citation

  • Kai Detlefsen & Wolfgang Härdle, 2006. "Forecasting the Term Structure of Variance Swaps," SFB 649 Discussion Papers SFB649DP2006-052, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2006-052
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-052.pdf
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    References listed on IDEAS

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    1. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    2. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
    3. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    4. Zellner, A., 1992. "Statistics, Science and Public Policy," Papers 92-21, California Irvine - School of Social Sciences.
    5. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    6. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
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    Cited by:

    1. Cayetano, Gea, 2007. "Studying the Properties of the Correlation Trades," MPRA Paper 22318, University Library of Munich, Germany.

    More about this item

    Keywords

    Term structure; Variance swap curve; Heston model; Nelson-Siegel curve; Semiparametric factor model;

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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