Neural networks (NN) and fuzzy logic systems (FLS) are used successfully for financial forecasting, credit rating and portfolio management. In search for more sophisticated modeling techniques a mixture of NN and FLS has proved to be worth consideration. We propose the novel constructive approach by which a neuro fuzzy network is built up with the help of a constrained optimizer. The mathematical motivation for such hybrid networks is presented, using the Kolmogorov theory of metric entropy. As an application of the proposed approach we build a neuro fuzzy network model which is able to explain the prices of call options written on the S&P 500 stock index. While option pricing theory typically requires a highly complex statistical model to capture the empirical pricing mechanism, our results indicate that this algorithm leads to more parsimonious functional specificationes which have a superior out-of-sample performance.
