This paper introduces a new estimation method of partially observed systems in which parameters are estimated by matching joint densities of observed data to joint densities of a model's observables reconstructed upon simulation of the whole system; both densities are recovered nonparametrically. The method offers computational advantages over existing techniques. It requires no auxiliary model with which one matches the observable characteristics of data, but only average kernels applied at once to simulated data. While the proposed method may be used in a potentially large number of applications arising in macroeconomics and finance, its usefulness is emphasized in relation to the estimation of models typically arising in continuous time finance, such as pure diffusions and jump-diffusion models.