This paper considers option valuation under finite mixture models in a discrete-time economy. Specifically, the Esscher transform is employed to select a pricing kernel. Novel finite mixture models with negative-shifted Gamma and negative-shifted inverse Gaussian distributions are developed. A hybrid finite mixture model that allows different parametric forms for component distributions is introduced to incorporate model uncertainty. An empirical characteristic function estimation method is employed to estimate the finite mixture models. Closed-form pricing formulas for a European call option are obtained for some finite mixture models. Empirical examples using data on the Bitcoin-USD prices are provided to illustrate an application of the proposed models to value Bitcoin options.
