Closed form integration of artificial neural networks with some applications - Andreas Gottschling; Christian Haefke; Halbert White (Deutsche Bank Research, 1999)
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: C45; G13; C63; 330; Option Pricing; Neural Networks; Nonparametric Density Estimation; Nichtparametrisches Verfahren; Neuronale Netze; Optionspreistheorie; Risiko; Theorie; Maximum-Likelihood-Methode; Value at Risk; Varianzanalyse