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VAR Modeling for Dynamic Semiparametric Factors of Volatility Strings

Author

Listed:
  • Ralf Brüggemann
  • Wolfgang Härdle
  • Julius Mungo
  • Carsten Trenkler

Abstract

The implied volatility of a European option as a function of strike price and time to maturity forms a volatility surface. Traders price according to the dynamics of this high dimensional surface. Recent developments that employ semiparametric models approximate the implied volatility surface (IVS) in a finite dimensional function space, allowing for a low dimensional factor representation of these dynamics. This paper presents an investigation into the stochastic properties of the factor loading times series using the vector autoregressive (VAR) framework and analyzes associated movements of these factors with movements in some macroeconomic variables of the Euro - economy.

Suggested Citation

  • Ralf Brüggemann & Wolfgang Härdle & Julius Mungo & Carsten Trenkler, 2006. "VAR Modeling for Dynamic Semiparametric Factors of Volatility Strings," SFB 649 Discussion Papers SFB649DP2006-011, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2006-011
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    References listed on IDEAS

    as
    1. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    2. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    3. Matthias Fengler & Wolfgang Härdle & Christophe Villa, 2003. "The Dynamics of Implied Volatilities: A Common Principal Components Approach," Review of Derivatives Research, Springer, vol. 6(3), pages 179-202, October.
    4. Szymon Borak & Matthias Fengler & Wolfgang Härdle, 2005. "DSFM fitting of Implied Volatility Surfaces," SFB 649 Discussion Papers SFB649DP2005-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    6. Toda, Hiro Y. & Yamamoto, Taku, 1995. "Statistical inference in vector autoregressions with possibly integrated processes," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 225-250.
    7. Pesaran, H. Hashem & Shin, Yongcheol, 1998. "Generalized impulse response analysis in linear multivariate models," Economics Letters, Elsevier, vol. 58(1), pages 17-29, January.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    10. Matthias Fengler & Wolfgang Härdle & Enno Mammen, 2005. "A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics," SFB 649 Discussion Papers SFB649DP2005-020, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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    Cited by:

    1. Wolfgang Karl Härdle,Piotr Majer & Melanie Schienle, 2012. "Yield Curve Modeling and Forecasting using Semiparametric Factor Dynamics," SFB 649 Discussion Papers SFB649DP2012-048, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Ostap Okhrin & Stefan Trück, 2015. "Editorial to the special issue on Applicable semiparametrics of computational statistics," Computational Statistics, Springer, vol. 30(3), pages 641-646, September.

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    More about this item

    Keywords

    Implied volatility surface; dynamic semiparametric factor model; unit root tests; vector autoregression; impulse responses;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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