Most contracts of barrier and lookback options specify discrete monitoring policies. However, unlike their continuous counterparts, discrete barrier and lookback options essentially have no analytical solution. For a broad class of models, including the classical Brownian model and jump-diffusion models, we show that the Laplace transforms of discrete barrier and lookback options can be obtained via a recursion involving only analytical formulae of standard European call and put options, thanks to Spitzer’s formula. The Laplace transforms can be numerically inverted to get option prices fast and accurately. Furthermore, the same method can be used to compute the hedging parameters (the greeks) of these products.