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Estimating market risk with neural networks

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  • Franke Jürgen
  • Diagne Mabouba

Abstract

We consider stochastic volatility models for discrete financial time series of the nonlinear autoregressive-ARCH type with exogenous components.We discuss how the trend and volatility functions determining the process may be estimated nonparametrically by least-squares fitting of neural networks or, more generally, of functions from other parametric classes having a universal approximation property. We prove consistency of the estimates under conditions on the rate of increase of function complexity. The procedure is applied to the problem of quantifying market risk, i.e. of calculating volatility or value-at-risk from the data taking not only the time series of interest but additional market information into account. As an application, we study some stock prices series and compare our approach with the common method based on fitting a GARCH(1,1)-model to the data

Suggested Citation

  • Franke Jürgen & Diagne Mabouba, 2006. "Estimating market risk with neural networks," Statistics & Risk Modeling, De Gruyter, vol. 24(2), pages 1-21, December.
    • Handle: RePEc:bpj:strimo:v:24:y:2006:i:2:p:21:n:2
    DOI: 10.1524/stnd.2006.24.2.233
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    References listed on IDEAS

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    1. Franke, Jurgen & Neumann, Michael H. & Stockis, Jean-Pierre, 2004. "Bootstrapping nonparametric estimators of the volatility function," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 189-218.
    2. Hardle, W. & Tsybakov, A., 1997. "Local polynomial estimators of the volatility function in nonparametric autoregression," Journal of Econometrics, Elsevier, vol. 81(1), pages 223-242, November.
    3. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
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    Cited by:

    1. Michael Kohler, 2008. "A regression-based smoothing spline Monte Carlo algorithm for pricing American options in discrete time," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(2), pages 153-178, May.
    2. Stockis, Jean-Pierre & Tadjuidje-Kamgaing, Joseph & Franke, Jürgen, 2008. "A note on the identifiability of the conditional expectation for the mixtures of neural networks," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 739-742, April.
    3. Kohler, Michael & Krzyzak, Adam & Walk, Harro, 2011. "Estimation of the essential supremum of a regression function," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 685-693, June.
    4. Jürgen Franke & Jean-Pierre Stockis & Joseph Tadjuidje, 2007. "Quantile Sieve Estimates For Time Series," SFB 649 Discussion Papers SFB649DP2007-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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