Closed Form Integration of Artificial Neural Networks with Some Applications to Finance
Christian Haefke () and
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Andreas Gottschling: Deutsche Bank Research
No 1080, Econometric Society World Congress 2000 Contributed Papers from Econometric Society
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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Working Paper: CLOSED FORM INTEGRATION OF ARTIFICIAL NEURAL NETWORKS WITH SOME APPLICATIONS TO FINANCE (2000)
Working Paper: Closed Form Integration of Artificial Neural Networks with Some Applications to Finance (1999)
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