In this paper, we develop an efficient algorithm to price options under discrete time GARCH processes. We propose a procedure based on dynamic programming coupled with piecewise polynomial approximation to compute the value of a given option, at all pricing dates and levels of the state vector. The method can be used for the large GARCH family of models based on real Gaussian innovations, and may accommodate all low-dimensional European as well as American derivatives. Numerical implementations show that this method competes very advantageously with other available pricing methods.