Closed form integration of artificial neural networks with some applications

Andreas Gottschling, Christian Haefke and Halbert White

No 99-9, Research Notes from Deutsche Bank Research

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.

Keywords: Option Pricing; Neural Networks; Nonparametric Density Estimation (search for similar items in EconPapers)
JEL-codes: C45 C63 G13 (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:zbw:dbrrns:999

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