Installment options are a generalization of compound options, where the holder periodically decides whether to keep an option alive or not by paying the installment. We propose a numerical procedure, based on dynamic programming coupled with piecewise polynomial approximations, to price installment options when the underlying asset price follows a GARCH process. Numerical experiments are carried out using data from the Australian Stock Exchange. Computed option prices under GARCH and Black-Scholes models are compared to traded prices.