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Neural network methods, coming from the brain science of cognitive theory and neurophysiology, offer a powerful alternative to linear and other existing non-linear models for forecasting, classification, and risk assessment in finance and economics.The objective of this thesis is to establish the use of Neural Networks and other related technologies like wavelets etc. for Quantitative Finance applications.This thesis evaluates the predictive accuracy with neural networks, encompassing forecasting, classification, and dimensionality reduction.This thesis also compares the performance of Neural network forecasting with conditional heteroscedastic models. Results show that Neural Networks can be effectively employed in forecasting of Exchange rate and Stock/Futures price, and in estimation of conditional and implied volatility of options. RBF networks do considerably better than MLP networks in extracting the information necessary to perform a good generalization from the training set.The number of hidden units used does not seem to have a straight relation with the forecast performance.