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Dynamic semiparametric factor models in risk neutral density estimation

  • Enzo Giacomini

    ()

  • Wolfgang Härdle
  • Volker Krätschmer

Dimension reduction techniques for functional data analysis model and approximate smooth random functions by lower dimensional objects. In many applications the focus of interest lies not only in dimension reduction but also in the dynamic behaviour of the lower dimensional objects. The most prominent dimension reduction technique - functional principal components analysis - however, does not model time dependences embedded in functional data. In this paper we use dynamic semiparametric factor models (DSFM) to reduce dimensionality and analyse the dynamic structure of unknown random functions by means of inference based on their lower dimensional representation. We apply DSFM to estimate the dynamic structure of risk neutral densities implied by prices of option on the DAX stock index.

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File URL: http://hdl.handle.net/10.1007/s10182-009-0115-4
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Article provided by Springer in its journal AStA Advances in Statistical Analysis.

Volume (Year): 93 (2009)
Issue (Month): 4 (December)
Pages: 387-402

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Handle: RePEc:spr:alstar:v:93:y:2009:i:4:p:387-402
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  1. Hernández-Hernández, Daniel & Schied, Alexander, 2007. "A control approach to robust utility maximization with logarithmic utility and time-consistent penalties," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 980-1000, August.
  2. Szymon Borak & Wolfgang Härdle & Enno Mammen & Byeong U. Park, 2007. "Time Series Modelling with Semiparametric Factor Dynamics," SFB 649 Discussion Papers SFB649DP2007-023, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, 04.
  4. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
  5. Fengler, Matthias R. & Härdle, Wolfgang & Mammen, Enno, 2003. "Implied volatility string dynamics," SFB 373 Discussion Papers 2003,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  6. Ralf Brüggemann & Wolfgang Härdle & Julius Mungo & Carsten Trenkler, 2008. "VAR Modeling for Dynamic Loadings Driving Volatility Strings," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(3), pages 361-381, Summer.
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