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Closed form integration of artificial neural networks with some applications

Author

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  • Gottschling, Andreas
  • Haefke, Christian
  • White, Halbert

Abstract

Many economic and econometric applications require the integration of functions lacking a closed form antiderivative, which is therefore a task that can only be solved by numerical methods. We propose a new family of probability densities that can be used as substitutes and have the property of closed form integrability. This is especially advantageous in cases where either the complexity of a problem makes numerical function evaluations very costly, or fast information extraction is required for time-varying environments. Our approach allows generally for nonparametric maximum likelihood density estimation and may thus find a variety of applications, two of which are illustrated briefly: Estimation of Value at Risk based on approximations to the density of stock returns; Recovering risk neutral densities for the valuation of options from the option price - strike price relation.

Suggested Citation

  • Gottschling, Andreas & Haefke, Christian & White, Halbert, 1999. "Closed form integration of artificial neural networks with some applications," Research Notes 99-9, Deutsche Bank Research.
    • Handle: RePEc:zbw:dbrrns:999
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    Cited by:

    1. John M. Maheu & Thomas H. McCurdy, 2002. "Nonlinear Features of Realized FX Volatility," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 668-681, November.

    More about this item

    Keywords

    Option Pricing; Neural Networks; Nonparametric Density Estimation;
    All these keywords.

    JEL classification:

    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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