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Closed Form Integration of Artificial Neural Networks with Some Applications to Finance

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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 to Finance," University of California at San Diego, Economics Working Paper Series qt0wz7n7nm, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt0wz7n7nm
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    Cited by:

    1. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    2. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
    3. 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.
    4. René Garcia & Eric Ghysels & Éric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.

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