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

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Author Info
Andreas Gottschling (Deutsche Bank)
Christian Haefke (Institute for Advanced Studies, Vienna)
Halbert White (University of California, San Diego)

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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

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Publisher Info
Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number 1999-24.

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Date of creation: 01 Nov 1999
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Handle: RePEc:cdl:ucsdec:1999-24

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Related research
Keywords: option pricing; neural networks; nonparametric density estimation;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October. [Downloadable!] (restricted)
  2. Patrice Bertail & Christian Haefke & Dimitris N. Politis & Halbert White, 2001. "A Subsampling Approach to Estimating the Distribution of Diversing Statistics with Application to Assessing Financial Market Risks," Economics Working Papers 599, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
  3. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-63, May. [Downloadable!] (restricted)
  4. Jon Danielsson, 1997. "Extreme Returns, Tail Estimation, and Value-at-Risk," FMG Discussion Papers dp273, Financial Markets Group. [Downloadable!] (restricted)
  5. Chung-Ming Kuan & Halbert White, 1992. "Artificial Neural Networks: An Econometric Perspective," University of California at San Diego, Economics Working Paper Series 92-11, Department of Economics, UC San Diego.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. John M. Maheu & Thomas H. McCurdy, 2001. "Nonlinear Features of Realized FX Volatility," CIRANO Working Papers 2001s-42, CIRANO. [Downloadable!]
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  2. René Garcia & Eric Ghysels & Éric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO. [Downloadable!]
  3. Yacine Ait-Sahalia & Jefferson Duarte, 2002. "Nonparametric Option Pricing under Shape Restrictions," NBER Working Papers 8944, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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