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We focus on the neural network training problem that could be used for price forecasting or other purposes in finance. We design and develop four different parallel and multithreaded backpropagation neural network algorithms: neuron and training set parallelism on a distributed memory architecture using MPI; loop-level (fine-grain) and coarse-grained parallelism in shared memory architecture using OpenMP. We have conducted various experiments to study the performance of these algorithms and compared our results with a traditional autoregression model to establish accuracy of our results. The comparison between our MPI and OpenMP results suggest that the training set parallelism performs better than all the other types of parallelism considered in the study.