Higher Order Neural Networks (HONN) are characterized with fast learning abilities, stronger approximation, greater storage capacity, higher fault tolerance capability and powerful mapping of single layer trainable weights. Since higher order terms are introduced, they provide nonlinear decision boundaries, hence offering better classification capability as compared to linear neuron. Nature-inspired optimization algorithms are capable of searching better than gradient descent-based search techniques. This paper develops some hybrid models by considering four HONNs such as Pi-Sigma, Sigma-Pi, Jordan Pi-Sigma neural network and Functional link artificial neural network as the base model. The optimal parameters of these neural nets are searched by a Particle swarm optimization, and a Genetic Algorithm. The models are employed to capture the extreme volatility, nonlinearity and uncertainty associated with stock data. Performance of these hybrid models is evaluated through prediction of one-step-ahead exchange rates of some real stock market. The efficiency of the models is compared with that of a Radial basis functional neural network, a multilayer perceptron, and a multi linear regression method and established their superiority. Friedman’s test and Nemenyi post-hoc test are conducted for statistical significance of the results.