Many applications in continuous-time financial economics require calculation of conditional moments or contingent claims prices, but such expressions are known in closed-form for only a few specific models. Power series (in the time variable) for these quantities are easily derived, but often fail to converge, even for very short time horizons. We characterize a large class of continuous-time non-a±ne conditional moment and contingent claim pricing problems with solutions that are analytic in the time variable, and that therefore can be represented by convergent power series. The ability to approximate solutions accurately and in closed-form simplifies the estimation of latent variable models, since the state vector must be extracted from observed quantities for many different parameter vectors during a typical estimation procedure.