Abstract In this note we reconsider the continuous time limit of the GARCH(1, 1) process. Let Y k and σ k 2 denote, respectively, the cumulative returns and the volatility processes. We consider the continuous time approximation of the couple (Y k, σ k 2). We show that, by choosing different parameterizations, as a function of the discrete interval h, we can obtain either a degenerate or a non-degenerate diffusion limit. We then show that GARCH(1, 1) processes can be obtained as Euler approximations of degenerate diffusions, while any Euler approximation of a non-degenerate diffusion is a stochastic volatility process.